{"id":"https://openalex.org/W4283011735","doi":"https://doi.org/10.1137/21m1417077","title":"Robust Connectivity of Graphs on Surfaces","display_name":"Robust Connectivity of Graphs on Surfaces","publication_year":2022,"publication_date":"2022-06-01","ids":{"openalex":"https://openalex.org/W4283011735","doi":"https://doi.org/10.1137/21m1417077"},"language":"en","primary_location":{"id":"doi:10.1137/21m1417077","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1417077","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2104.12030","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079359533","display_name":"Peter Bradshaw","orcid":"https://orcid.org/0000-0003-2562-6141"},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Peter Bradshaw","raw_affiliation_strings":["Simon Fraser University, Burnaby, BC, Canada"],"raw_orcid":"https://orcid.org/0000-0003-2562-6141","affiliations":[{"raw_affiliation_string":"Simon Fraser University, Burnaby, BC, Canada","institution_ids":["https://openalex.org/I18014758"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027217082","display_name":"Tom\u00e1\u0161 Masa\u0159\u00edk","orcid":"https://orcid.org/0000-0001-8524-4036"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tom\u00e1\u0161 Masa\u0159\u00edk","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-8524-4036","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111560027","display_name":"Jana Novotn\u00e1","orcid":null},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]},{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["CA","PL"],"is_corresponding":false,"raw_author_name":"Jana Novotn\u00e1","raw_affiliation_strings":["University of Warsaw, Warsaw, Poland","Simon Fraser University, Burnaby, BC, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]},{"raw_affiliation_string":"Simon Fraser University, Burnaby, BC, Canada","institution_ids":["https://openalex.org/I18014758"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085438222","display_name":"Ladislav Stacho","orcid":null},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Ladislav Stacho","raw_affiliation_strings":["Simon Fraser University, Burnaby, BC, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Simon Fraser University, Burnaby, BC, Canada","institution_ids":["https://openalex.org/I18014758"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1326,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.44033657,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"36","issue":"2","first_page":"1416","last_page":"1435"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9894999861717224,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8069630265235901},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7161693572998047},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6335433125495911},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.6287705302238464},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4932026267051697},{"id":"https://openalex.org/keywords/degeneracy","display_name":"Degeneracy (biology)","score":0.470601886510849},{"id":"https://openalex.org/keywords/dominating-set","display_name":"Dominating set","score":0.45984116196632385},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4404013454914093},{"id":"https://openalex.org/keywords/arboricity","display_name":"Arboricity","score":0.4326099157333374},{"id":"https://openalex.org/keywords/spanning-tree","display_name":"Spanning tree","score":0.42619284987449646},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.41077035665512085},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3999272286891937},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.15402761101722717}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8069630265235901},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7161693572998047},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6335433125495911},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.6287705302238464},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4932026267051697},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.470601886510849},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.45984116196632385},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4404013454914093},{"id":"https://openalex.org/C83204008","wikidata":"https://www.wikidata.org/wiki/Q4784907","display_name":"Arboricity","level":4,"score":0.4326099157333374},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.42619284987449646},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.41077035665512085},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3999272286891937},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.15402761101722717},{"id":"https://openalex.org/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/21m1417077","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1417077","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2104.12030","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2104.12030","pdf_url":"https://arxiv.org/pdf/2104.12030","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2104.12030","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2104.12030","pdf_url":"https://arxiv.org/pdf/2104.12030","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","score":0.4300000071525574,"display_name":"Life in Land"}],"awards":[{"id":"https://openalex.org/G3095692980","display_name":null,"funder_award_id":"R611368","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G548662704","display_name":null,"funder_award_id":"R611450","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320323873","display_name":"Uniwersytet Warszawski","ror":"https://ror.org/039bjqg32"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W69045515","https://openalex.org/W89315147","https://openalex.org/W564518845","https://openalex.org/W1969029923","https://openalex.org/W1971818177","https://openalex.org/W1999519812","https://openalex.org/W2011105641","https://openalex.org/W2016241195","https://openalex.org/W2025085400","https://openalex.org/W2035440971","https://openalex.org/W2040813792","https://openalex.org/W2048653445","https://openalex.org/W2064084823","https://openalex.org/W2078178103","https://openalex.org/W2129166227","https://openalex.org/W2180968341","https://openalex.org/W2301667118","https://openalex.org/W2519445075","https://openalex.org/W2548944478","https://openalex.org/W2558789634","https://openalex.org/W2620553479","https://openalex.org/W2776000100","https://openalex.org/W2964130394","https://openalex.org/W2964217904","https://openalex.org/W2969413889","https://openalex.org/W3084987570","https://openalex.org/W3099663620","https://openalex.org/W3157059698","https://openalex.org/W3177562069","https://openalex.org/W4213087285","https://openalex.org/W4301005547"],"related_works":["https://openalex.org/W2923904201","https://openalex.org/W4289766102","https://openalex.org/W2809699696","https://openalex.org/W2061460135","https://openalex.org/W4288262792","https://openalex.org/W3197826830","https://openalex.org/W172647603","https://openalex.org/W3166626209","https://openalex.org/W4225767671","https://openalex.org/W2100628151"],"abstract_inverted_index":{"Let":[0],"$\\Lambda(T)$":[1,29],"denote":[2],"the":[3,50,57,64,84,111,141,175,184,252,269,282,304,308],"set":[4,61],"of":[5,22,72,80,87,113,140,235,249,255,258,272,285,296,322,326,362],"leaves":[6],"in":[7,83,132,138,224,241,278,335],"a":[8,18,23,45,69,117,167,171,203,245,265,279,323],"tree":[9,20,205],"$T$.":[10],"One":[11],"natural":[12],"problem":[13,36,52],"is":[14,30,37,44,66,82,202],"to":[15,67,106,110,209,220,290],"look":[16],"for":[17,170,238,251],"spanning":[19,204],"$T$":[21],"given":[24],"graph":[25,103,172,354],"$G$":[26,81,207],"such":[27,76],"that":[28,77,286,351],"as":[31,33,56,180,183],"large":[32,293],"possible.":[34],"This":[35],"called":[38,174],"maximum":[39],"leaf":[40],"number,":[41],"and":[42,127,147,178,281,328,338],"it":[43],"well-known":[46],"NP-hard":[47],"problem.":[48],"Equivalently,":[49],"same":[51],"can":[53,299],"be":[54,300],"formulated":[55],"minimum":[58,185],"connected":[59],"dominating":[60],"problem,":[62],"where":[63,198],"task":[65],"find":[68],"smallest":[70],"subset":[71],"vertices":[73,357],"$D\\subseteq":[74],"V(G)$":[75],"every":[78,352],"vertex":[79],"closed":[85],"neighborhood":[86],"$D$.":[88],"Throughout":[89],"recent":[90],"decades,":[91],"these":[92],"two":[93],"equivalent":[94,320],"problems":[95,108],"have":[96],"received":[97],"considerable":[98],"attention,":[99],"ranging":[100],"from":[101,303],"pure":[102],"theoretic":[104],"questions":[105],"practical":[107],"related":[109],"construction":[112],"wireless":[114],"networks.":[115],"Recently,":[116],"similar":[118],"but":[119],"stronger":[120],"notion":[121],"was":[122,217],"defined":[123,182],"by":[124],"Bradshaw,":[125],"Masa\u0159\u00edk,":[126],"Stacho":[128],"[Flexible":[129],"list":[130],"colorings":[131],"graphs":[133,239,257,273,298],"with":[134,274],"special":[135],"degeneracy":[136],"conditions,":[137],"Proceedings":[139],"31st":[142],"International":[143],"Symposium":[144],"on":[145,206,332,355],"Algorithms":[146],"Computation":[148],"(ISAAC":[149],"2020),":[150],"LIPIcs.":[151],"Leibniz":[152],"Int.":[153],"Proc.":[154],"Inform.":[155],"181,":[156],"Schloss":[157],"Dagstuhl.":[158],"Leibniz-Zent.":[159],"Inform.,":[160],"Wadern,":[161],"2020,":[162],"article":[163],"31].":[164],"They":[165],"introduced":[166],"new":[168],"invariant":[169],"$G$,":[173],"robust":[176,215,236,253,270],"connectivity":[177,216,237,254,271,284],"written":[179],"$\\kappa_\\rho(G)$,":[181],"value":[186],"$\\frac{|R":[187],"\\cap":[188,212],"\\Lambda":[189],"(T)|}{|R|}$":[190],"taken":[191],"over":[192],"all":[193],"nonempty":[194],"subsets":[195],"$R\\subseteq":[196],"V(G)$,":[197],"$T":[199],"=":[200],"T(R)$":[201],"chosen":[208],"maximize":[210],"$|R":[211],"\\Lambda(T)|$.":[213],"Large":[214],"originally":[218],"used":[219],"show":[221],"flexible":[222],"choosability":[223],"nonregular":[225],"graphs.":[226],"In":[227],"this":[228,316],"paper,":[229],"we":[230,263],"investigate":[231],"some":[232],"interesting":[233],"properties":[234],"embedded":[240,297],"surfaces.":[242],"We":[243],"prove":[244],"tight":[246],"asymptotic":[247],"bound":[248],"$\\Omega(\\gamma^{-\\frac{1}{r}})$":[250],"$r$-connected":[256],"Euler":[259],"genus":[260],"$\\gamma$.":[261],"Moreover,":[262],"give":[264],"surprising":[266],"connection":[267,317],"between":[268],"an":[275,319,359],"edge-maximal":[276],"embedding":[277],"surface":[280,283,305,309],"surface,":[287],"which":[288,349],"describes":[289],"what":[291],"extent":[292],"induced":[294,360],"subgraphs":[295],"cut":[301],"out":[302],"without":[306],"splitting":[307],"into":[310],"multiple":[311],"parts.":[312],"For":[313],"planar":[314,333,353],"graphs,":[315,334],"provides":[318],"formulation":[321],"long-standing":[324],"conjecture":[325,331],"Albertson":[327],"Berman":[329],"[A":[330],"Graph":[336],"Theory":[337],"Related":[339],"Topics,":[340],"Academic":[341],"Press,":[342],"San":[343],"Diego,":[344],"CA,":[345],"1979,":[346],"p.":[347],"57],":[348],"states":[350],"$n$":[356],"contains":[358],"forest":[361],"size":[363],"at":[364],"least":[365],"$n/2$.":[366]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
