{"id":"https://openalex.org/W2110861431","doi":"https://doi.org/10.1137/110849407","title":"Bounds on the Maximum Multiplicity of Some Common Geometric Graphs","display_name":"Bounds on the Maximum Multiplicity of Some Common Geometric Graphs","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2110861431","doi":"https://doi.org/10.1137/110849407","mag":"2110861431"},"language":"en","primary_location":{"id":"doi:10.1137/110849407","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110849407","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":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091313409","display_name":"Adrian Dumitrescu","orcid":"https://orcid.org/0000-0002-1118-0321"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Adrian Dumitrescu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055531990","display_name":"Andr\u00e9 Schulz","orcid":"https://orcid.org/0000-0002-2134-4852"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andr\u00e9 Schulz","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038764657","display_name":"Adam Sheffer","orcid":"https://orcid.org/0000-0003-3418-5122"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Adam Sheffer","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5030799674","display_name":"Csaba D. T\u00f3th","orcid":"https://orcid.org/0000-0002-8769-3190"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Csaba D. T\u00f3th","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5091313409"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":15.3922,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.99078341,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"27","issue":"2","first_page":"802","last_page":"826"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.8059999942779541,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.8059999942779541,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.10819999873638153,"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":0.027899999171495438,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.9118266105651855},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8035608530044556},{"id":"https://openalex.org/keywords/general-position","display_name":"General position","score":0.7837749123573303},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7057050466537476},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.7039749622344971},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.5724231004714966},{"id":"https://openalex.org/keywords/spanning-tree","display_name":"Spanning tree","score":0.5552159547805786},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5210249423980713},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3620803654193878},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12391170859336853}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9118266105651855},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8035608530044556},{"id":"https://openalex.org/C150397156","wikidata":"https://www.wikidata.org/wiki/Q591310","display_name":"General position","level":2,"score":0.7837749123573303},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7057050466537476},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.7039749622344971},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.5724231004714966},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.5552159547805786},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5210249423980713},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3620803654193878},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12391170859336853},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/110849407","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110849407","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1656332081","https://openalex.org/W1965976352","https://openalex.org/W1990566310","https://openalex.org/W2000008376","https://openalex.org/W2013115769","https://openalex.org/W2057690024","https://openalex.org/W2071731426","https://openalex.org/W2079698947","https://openalex.org/W2085110997","https://openalex.org/W2085179971","https://openalex.org/W2086526821","https://openalex.org/W2096398399","https://openalex.org/W2109075893","https://openalex.org/W2152141013","https://openalex.org/W2163448076","https://openalex.org/W2569928643","https://openalex.org/W4238913003"],"related_works":["https://openalex.org/W238609530","https://openalex.org/W2734192830","https://openalex.org/W4205377127","https://openalex.org/W3016395638","https://openalex.org/W4230581126","https://openalex.org/W1636163329","https://openalex.org/W1978344479","https://openalex.org/W1967689857","https://openalex.org/W315834793","https://openalex.org/W4288090900"],"abstract_inverted_index":{"We":[0,45,110,182,201,328],"obtain":[1,111],"new":[2,48,113],"lower":[3,49,114,184],"and":[4,42,161,191,199,255,292,321],"upper":[5,149],"bounds":[6,185,315],"for":[7,52,118,140,153,186,214,316,344],"the":[8,25,53,90,96,100,119,126,154,169,187,204,228,243,260,277,317],"maximum":[9,54,190],"multiplicity":[10],"of":[11,56,60,116,121,125,130,151,156,189,206,230,245,262,279,284,319,334],"some":[12,325],"weighted":[13,193],"and,":[14],"respectively,":[15],"nonweighted":[16],"common":[17],"geometric":[18,194],"graphs":[19,195],"drawn":[20],"on":[21],"$n$":[22,61,166,213],"points":[23,33,62,167,215,303,308],"in":[24,27,63,168,171,212,216,237,253,271,304,309],"plane":[26,170],"general":[28,64,172,217],"position":[29,65,173,311],"(with":[30],"no":[31],"three":[32],"collinear):":[34],"perfect":[35,248,265],"matchings,":[36],"spanning":[37,39,123,179,197,282],"trees,":[38,198],"cycles":[40],"(tours),":[41],"triangulations.":[43,87],"(i)":[44],"present":[46],"a":[47,58,73,112,147,285,331],"bound":[50,91,115,150],"construction":[51],"number":[55,120,155,188,205,229,244,261,278,318],"triangulations":[57],"set":[59,287],"can":[66,209,234,250,267,288,298],"have.":[67],"In":[68],"particular,":[69],"we":[70,163,225,257,294,312],"show":[71,164,202,226,258,295],"that":[72,165,203,227,242,259,276,296],"generalized":[74],"double":[75,101,127],"chain":[76,103,128],"formed":[77],"by":[78,95,105],"two":[79,131],"almost":[80],"convex":[81,132,305,310],"chains":[82],"admits":[83],"$\\Omega":[84,92],"(8.65^n)$":[85],"different":[86],"This":[88],"improves":[89],"(8.48^n)$":[93],"achieved":[94],"previous":[97,135],"best":[98],"construction,":[99],"zig-zag":[102],"studied":[104],"Aichholzer":[106],"et":[107],"al.":[108],"(ii)":[109],"$\\Omega(12.00^n)$":[117],"noncrossing":[122,178,232,247,264,281],"trees":[124,283],"composed":[129],"chains.":[133],"The":[134],"bound,":[136],"$\\Omega(10.42^n)$,":[137],"stood":[138],"unchanged":[139],"more":[141],"than":[142],"10":[143],"years.":[144],"(iii)":[145],"Using":[146],"recent":[148],"$30^n$":[152],"triangulations,":[157],"due":[158],"to":[159],"Sharir":[160],"Sheffer,":[162],"admit":[174],"at":[175],"most":[176],"$O(68.62^n)$":[177],"cycles.":[180],"(iv)":[181],"derive":[183],"minimum":[192],"(matchings,":[196],"tours).":[200],"shortest":[207,246,322],"tours":[208,220,233,323],"be":[210,235,251,268,289,299],"exponential":[211,236,252,270],"position.":[218,306],"These":[219],"are":[221],"automatically":[222],"noncrossing.":[223],"Likewise,":[224],"longest":[231,263,280,320,335],"$n$.":[238,272],"It":[239,273],"was":[240,274],"known":[241,275],"matchings":[249,266],"$n$,":[254],"here":[256,293],"also":[269,300,329],"point":[286],"exponentially":[290],"large,":[291],"this":[297],"realized":[301],"with":[302,324],"For":[307],"re-derive":[313],"tight":[314],"simpler":[326],"arguments.":[327],"give":[330],"combinatorial":[332],"characterization":[333],"tours,":[336],"which":[337],"yields":[338],"an":[339],"$O(n\\log":[340],"n)$":[341],"time":[342],"algorithm":[343],"computing":[345],"them.":[346]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":2}],"updated_date":"2026-03-03T08:47:05.690250","created_date":"2025-10-10T00:00:00"}
