{"id":"https://openalex.org/W7127585915","doi":"https://doi.org/10.1016/j.ejc.2026.104348","title":"Polynomials counting group colorings in graphs","display_name":"Polynomials counting group colorings in graphs","publication_year":2026,"publication_date":"2026-02-04","ids":{"openalex":"https://openalex.org/W7127585915","doi":"https://doi.org/10.1016/j.ejc.2026.104348"},"language":"en","primary_location":{"id":"doi:10.1016/j.ejc.2026.104348","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.ejc.2026.104348","pdf_url":null,"source":{"id":"https://openalex.org/S204851967","display_name":"European Journal of Combinatorics","issn_l":"0195-6698","issn":["0195-6698","1095-9971"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.ejc.2026.104348","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015544622","display_name":"Houshan Fu","orcid":"https://orcid.org/0000-0003-4541-4058"},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Houshan Fu","raw_affiliation_strings":["School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, Guangdong, PR China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, Guangdong, PR China","institution_ids":["https://openalex.org/I37987034"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015544622"],"corresponding_institution_ids":["https://openalex.org/I37987034"],"apc_list":{"value":2880,"currency":"USD","value_usd":2880},"apc_paid":{"value":2880,"currency":"USD","value_usd":2880},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.29972845,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"134","issue":null,"first_page":"104348","last_page":"104348"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.35530000925064087,"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":0.35530000925064087,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.17749999463558197,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.0949999988079071,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5889000296592712},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.5436000227928162},{"id":"https://openalex.org/keywords/chromatic-polynomial","display_name":"Chromatic polynomial","score":0.5142999887466431},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.49720001220703125},{"id":"https://openalex.org/keywords/matroid","display_name":"Matroid","score":0.45010000467300415},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4027000069618225},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.3971000015735626}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9117000102996826},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8549000024795532},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5889000296592712},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5436000227928162},{"id":"https://openalex.org/C126385604","wikidata":"https://www.wikidata.org/wiki/Q1087609","display_name":"Chromatic polynomial","level":3,"score":0.5142999887466431},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.49720001220703125},{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.45010000467300415},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43380001187324524},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4027000069618225},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3971000015735626},{"id":"https://openalex.org/C14447369","wikidata":"https://www.wikidata.org/wiki/Q7857002","display_name":"Tutte polynomial","level":5,"score":0.3718000054359436},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3452000021934509},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.33880001306533813},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.28450000286102295},{"id":"https://openalex.org/C169827030","wikidata":"https://www.wikidata.org/wiki/Q2294516","display_name":"Dual graph","level":4,"score":0.28450000286102295},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.2736999988555908},{"id":"https://openalex.org/C44115641","wikidata":"https://www.wikidata.org/wiki/Q918099","display_name":"Ramsey's theorem","level":3,"score":0.2646999955177307}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.ejc.2026.104348","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.ejc.2026.104348","pdf_url":null,"source":{"id":"https://openalex.org/S204851967","display_name":"European Journal of Combinatorics","issn_l":"0195-6698","issn":["0195-6698","1095-9971"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/j.ejc.2026.104348","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.ejc.2026.104348","pdf_url":null,"source":{"id":"https://openalex.org/S204851967","display_name":"European Journal of Combinatorics","issn_l":"0195-6698","issn":["0195-6698","1095-9971"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1790904978","display_name":null,"funder_award_id":"12301424","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1990070825","https://openalex.org/W2008263650","https://openalex.org/W2011470163","https://openalex.org/W2011940048","https://openalex.org/W2023859733","https://openalex.org/W2029317359","https://openalex.org/W2040661328","https://openalex.org/W2045832174","https://openalex.org/W2050064400","https://openalex.org/W2055828174","https://openalex.org/W2079944966","https://openalex.org/W2085349558","https://openalex.org/W2088122222","https://openalex.org/W2092653160","https://openalex.org/W2093572455","https://openalex.org/W2155060804","https://openalex.org/W2158959301","https://openalex.org/W2314361409","https://openalex.org/W2319873605","https://openalex.org/W2332615042","https://openalex.org/W2332969099","https://openalex.org/W2963000969","https://openalex.org/W2963621666","https://openalex.org/W2964127965","https://openalex.org/W3010683767","https://openalex.org/W3167054464","https://openalex.org/W3210298079","https://openalex.org/W4210769083","https://openalex.org/W4249593303","https://openalex.org/W4250153949","https://openalex.org/W4250476093","https://openalex.org/W4386823040","https://openalex.org/W4403389910"],"related_works":[],"abstract_inverted_index":{"Jaeger":[0],"et":[1],"al.":[2],"in":[3,15,100,106,117,144,293,381],"1992":[4],"introduced":[5,92],"group":[6,13,194],"coloring":[7,43],"as":[8],"the":[9,93,112,126,131,180,210,277,281,308,328,366],"dual":[10],"concept":[11,269],"to":[12,85,96,114,161,270,327,340],"connectivity":[14],"graphs.":[16],"Let":[17],"A":[18,31,41,51,55,184,195,207,253],"be":[19],"an":[20,34,53,154,223],"additive":[21],"Abelian":[22,193],"group,":[23],"f":[24,57,71,186,200,215,218,255],":":[25,45,201],"E":[26,202],"(":[27,47,54,62,67,72,135,172,183,203,237,241,252,287,295,356,370],"G":[28,39,48,136,157,173,190,204,238,242,288,296,353,371],")":[29,49,58,64,69,74,141,178,187,205,239,247,256,289,301,358,376],"\u2192":[30,50,206],"and":[32,109,130,199,258,319,343,379],"D":[33,88,213],"orientation":[35],"of":[36,103,146,156,182,189,196,280,283,310,352,368],"a":[37,249,333],"graph":[38,129],".":[40,89,167,221],"vertex":[42],"c":[44,61,66,236],"V":[46,286],"is":[52,153,225,248],",":[56,137,164,174,185,214,243,254,297,365,372],"-coloring":[59],"if":[60],"v":[63,82,86],"\u2212":[65,235,291],"u":[68,81,84],"\u2260":[70],"e":[73,79,357,364],"for":[75,191,347,361],"each":[76],"oriented":[77],"edge":[78],"=":[80,359],"from":[83,158,337],"under":[87],"Kochol":[90,107,118],"recently":[91],"assigning":[94,155,211,224,350],"polynomial":[95,133,250],"count":[97],"nowhere-zero":[98,104,261],"chains":[99],"graphs-nonhomogeneous":[101],"analogues":[102],"flows":[105],"(2022),":[108],"later":[110],"extended":[111],"approach":[113],"regular":[115],"matroids":[116],"(2024).":[119],"Motivated":[120],"by":[121,217,264],"Kochol\u2019s":[122,229],"work,":[123,230],"we":[124,231,274,331],"define":[125],"\u03b1":[127,138,147,152,175,212,220,244,298,306,311,323,351,355,373],"-compatible":[128,148,312,324],"cycle-assigning":[132,341],"P":[134,171,240,294,369],";":[139,176,245,299,374],"k":[140,143,177,198,234,246,284,300,375],"at":[142],"terms":[145],"spanning":[149,313],"subgraphs,":[150],"where":[151],"its":[159],"cycles":[160],"{":[162],"0":[163],"1":[165,360],"}":[166],"We":[168],"prove":[169],"that":[170,209,233,276,315,346],"evaluates":[179],"number":[181,309],"-colorings":[188],"any":[192,348],"order":[197],"such":[208],"given":[216],"equals":[219,307],"Such":[222],"admissible.":[226],"Based":[227],"on":[228],"derive":[232],"enumerating":[251],"-tensions":[257],"counting":[259],"specific":[260],"chains.":[262],"Furthermore,":[263],"extending":[265],"Whitney\u2019s":[266],"broken":[267,271,322],"cycle":[268],"compatible":[272],"cycles,":[273],"show":[275,345],"absolute":[278],"value":[279],"coefficient":[282],"|":[285,290],"i":[292,317],"associated":[302],"with":[303,354],"admissible":[304,338,349],"assignings":[305,339],"subgraphs":[314],"have":[316],"edges":[318],"contain":[320],"no":[321],"cycles.":[325],"According":[326],"combinatorial":[329],"explanation,":[330],"establish":[332],"unified":[334],"order-preserving":[335],"relation":[336],"polynomials,":[342],"further":[344],"every":[362],"loop":[363],"coefficients":[367],"are":[377],"nonzero":[378],"alternate":[380],"sign.":[382]},"counts_by_year":[],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2026-02-06T00:00:00"}
