{"id":"https://openalex.org/W7171566604","doi":"https://doi.org/10.48550/arxiv.2607.23754","title":"Set-defined graph classes: $\u03c7$-boundedness meets tropical algebra","display_name":"Set-defined graph classes: $\u03c7$-boundedness meets tropical algebra","publication_year":2026,"publication_date":"2026-07-26","ids":{"openalex":"https://openalex.org/W7171566604","doi":"https://doi.org/10.48550/arxiv.2607.23754"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2607.23754","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.23754","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2607.23754","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5143808479","display_name":"Sarosh Adenwalla","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Adenwalla, Sarosh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130327051","display_name":"Samuel Braunfeld","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Braunfeld, Samuel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030391868","display_name":"Tom\u00e1\u0161 Hons","orcid":"https://orcid.org/0009-0001-7202-8681"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hons, Tom\u00e1\u0161","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067885700","display_name":"John Sylvester","orcid":"https://orcid.org/0000-0002-6543-2934"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sylvester, John","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5047948708","display_name":"Viktor Zamaraev","orcid":"https://orcid.org/0000-0001-5755-4141"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zamaraev, Viktor","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.512499988079071,"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":0.512499988079071,"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":0.3779999911785126,"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/T10142","display_name":"Formal Methods in Verification","score":0.024800000712275505,"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/bounded-function","display_name":"Bounded function","score":0.5805000066757202},{"id":"https://openalex.org/keywords/clique-width","display_name":"Clique-width","score":0.4316999912261963},{"id":"https://openalex.org/keywords/adjacency-list","display_name":"Adjacency list","score":0.4244000017642975},{"id":"https://openalex.org/keywords/graph-homomorphism","display_name":"Graph homomorphism","score":0.40220001339912415},{"id":"https://openalex.org/keywords/cograph","display_name":"Cograph","score":0.3977999985218048},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.39169999957084656},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3828999996185303},{"id":"https://openalex.org/keywords/graph-property","display_name":"Graph property","score":0.3702000081539154},{"id":"https://openalex.org/keywords/graph-coloring","display_name":"Graph coloring","score":0.36899998784065247}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7487000226974487},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6884999871253967},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.59579998254776},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5805000066757202},{"id":"https://openalex.org/C5737132","wikidata":"https://www.wikidata.org/wiki/Q1101814","display_name":"Clique-width","level":5,"score":0.4316999912261963},{"id":"https://openalex.org/C110484373","wikidata":"https://www.wikidata.org/wiki/Q264398","display_name":"Adjacency list","level":2,"score":0.4244000017642975},{"id":"https://openalex.org/C7036158","wikidata":"https://www.wikidata.org/wiki/Q3385162","display_name":"Graph homomorphism","level":5,"score":0.40220001339912415},{"id":"https://openalex.org/C59824394","wikidata":"https://www.wikidata.org/wiki/Q5141281","display_name":"Cograph","level":5,"score":0.3977999985218048},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.39169999957084656},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3828999996185303},{"id":"https://openalex.org/C64339825","wikidata":"https://www.wikidata.org/wiki/Q722659","display_name":"Graph property","level":5,"score":0.3702000081539154},{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.36899998784065247},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.3653999865055084},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.33799999952316284},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.30390000343322754},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.3018999993801117},{"id":"https://openalex.org/C70488441","wikidata":"https://www.wikidata.org/wiki/Q5504427","display_name":"Friendship graph","level":5,"score":0.3018999993801117},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.3009999990463257},{"id":"https://openalex.org/C8554925","wikidata":"https://www.wikidata.org/wiki/Q3893853","display_name":"Split graph","level":5,"score":0.2946000099182129},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.28850001096725464},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.28690001368522644},{"id":"https://openalex.org/C32972407","wikidata":"https://www.wikidata.org/wiki/Q1187620","display_name":"Perfect graph","level":5,"score":0.2784999907016754},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.27489998936653137},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.27480000257492065},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.27379998564720154},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C68103157","wikidata":"https://www.wikidata.org/wiki/Q569347","display_name":"Graph product","level":5,"score":0.2667999863624573},{"id":"https://openalex.org/C187407849","wikidata":"https://www.wikidata.org/wiki/Q6889712","display_name":"Modular decomposition","level":5,"score":0.2565999925136566}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2607.23754","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.23754","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2607.23754","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.23754","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,37],"study":[1],"set-defined":[2,68,118,122,171,222],"graph":[3,28,65,243],"classes:":[4],"hereditary":[5],"classes":[6,24],"whose":[7,224],"vertices":[8],"are":[9,41],"assigned":[10],"fixed-length":[11],"numerical":[12],"tuples,":[13],"with":[14,195],"adjacency":[15,34],"determined":[16],"solely":[17],"by":[18,129],"equality":[19,135],"patterns":[20],"among":[21],"coordinates.":[22],"These":[23],"arise":[25],"in":[26,50,66,80,117,198,216],"structural":[27,242],"theory,":[29,244],"communication":[30],"complexity,":[31],"logic,":[32],"and":[33,188,208,238,247],"labeling":[35],"schemes.":[36],"ask":[38],"when":[39,45],"they":[40],"$\u03c7$-bounded,":[42],"that":[43,95],"is,":[44,96],"chromatic":[46,156],"number":[47,54,75,91],"is":[48,145,226],"bounded":[49,79,90,106],"terms":[51],"of":[52,76,88,92,108,125,153,168,175,184,205,235],"clique":[53,82],"throughout":[55],"the":[56,112,176,180],"class.":[57,177],"First,":[58],"we":[59,137,159],"prove":[60,138],"a":[61,67,74,86,89,99,102,130,139,165,169,193,221,232],"decomposition":[62],"theorem:":[63],"every":[64,142,202,210],"class":[69,144,223],"can":[70,213],"be":[71,214],"partitioned":[72],"into":[73],"parts":[77],"polynomially":[78,147],"its":[81,189],"number,":[83],"each":[84],"inducing":[85],"union":[87],"shift-colorable":[93,109],"graphs,":[94],"graphs":[97,110,127,152],"admitting":[98],"homomorphism":[100],"to":[101,115,182,228],"shift":[103,151],"graph.":[104],"Thus":[105],"unions":[107],"form":[111],"fundamental":[113],"obstruction":[114],"$\u03c7$-boundedness":[116,174],"classes.":[119],"For":[120],"full":[121,170],"classes,":[123],"consisting":[124],"all":[126],"realizable":[128],"fixed":[131],"Boolean":[132],"rule":[133],"on":[134],"patterns,":[136],"stronger":[140],"dichotomy:":[141],"such":[143],"either":[146],"$\u03c7$-bounded":[148],"or":[149],"contains":[150],"arbitrarily":[154],"large":[155],"number.":[157],"Moreover,":[158],"provide":[160],"an":[161],"algorithm":[162],"that,":[163],"given":[164],"Boolean-function":[166],"description":[167],"class,":[172],"decides":[173],"It":[178],"reduces":[179],"problem":[181],"feasibility":[183,237],"tropical":[185,206,236,245],"linear":[186],"programs,":[187],"correctness":[190],"follows":[191],"from":[192],"duality":[194],"winning":[196],"strategies":[197],"mean-payoff":[199,211],"games.":[200],"Conversely,":[201],"integer":[203],"system":[204],"inequalities,":[207],"hence":[209],"game,":[212],"encoded":[215],"strongly":[217],"polynomial":[218],"time":[219],"as":[220],"non-$\u03c7$-boundedness":[225],"equivalent":[227],"feasibility.":[229],"This":[230],"provides":[231],"graph-theoretic":[233],"counterpart":[234],"mean-payoff-game":[239],"solvability,":[240],"linking":[241],"algebra,":[246],"game-theoretic":[248],"algorithms.":[249]},"counts_by_year":[],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2026-07-29T00:00:00"}
