{"id":"https://openalex.org/W4412364984","doi":"https://doi.org/10.1007/s00373-025-02938-1","title":"Counting Subgraphs of Coloring Graphs","display_name":"Counting Subgraphs of Coloring Graphs","publication_year":2025,"publication_date":"2025-07-12","ids":{"openalex":"https://openalex.org/W4412364984","doi":"https://doi.org/10.1007/s00373-025-02938-1"},"language":"en","primary_location":{"id":"doi:10.1007/s00373-025-02938-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-025-02938-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-025-02938-1.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00373-025-02938-1.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071847515","display_name":"Shamil Asgarli","orcid":"https://orcid.org/0000-0003-3165-8297"},"institutions":[{"id":"https://openalex.org/I16269868","display_name":"Santa Clara University","ror":"https://ror.org/03ypqe447","country_code":"US","type":"education","lineage":["https://openalex.org/I16269868"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Shamil Asgarli","raw_affiliation_strings":["Department of Mathematics and Computer Science, Santa Clara University, Santa Clara, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Santa Clara University, Santa Clara, USA","institution_ids":["https://openalex.org/I16269868"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031710649","display_name":"Sara Krehbiel","orcid":"https://orcid.org/0000-0002-3662-4005"},"institutions":[{"id":"https://openalex.org/I16269868","display_name":"Santa Clara University","ror":"https://ror.org/03ypqe447","country_code":"US","type":"education","lineage":["https://openalex.org/I16269868"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sara Krehbiel","raw_affiliation_strings":["Department of Mathematics and Computer Science, Santa Clara University, Santa Clara, USA"],"raw_orcid":"https://orcid.org/0000-0002-3662-4005","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Santa Clara University, Santa Clara, USA","institution_ids":["https://openalex.org/I16269868"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102885781","display_name":"Howard Levinson","orcid":"https://orcid.org/0000-0003-4933-4645"},"institutions":[{"id":"https://openalex.org/I70571728","display_name":"Oberlin College","ror":"https://ror.org/05ac26z88","country_code":"US","type":"education","lineage":["https://openalex.org/I70571728"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Howard W. Levinson","raw_affiliation_strings":["Department of Computer Science, Oberlin College, Oberlin, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Oberlin College, Oberlin, USA","institution_ids":["https://openalex.org/I70571728"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028867644","display_name":"Heather M. Russell","orcid":"https://orcid.org/0000-0003-1256-2150"},"institutions":[{"id":"https://openalex.org/I158012942","display_name":"University of Richmond","ror":"https://ror.org/03y71xh61","country_code":"US","type":"education","lineage":["https://openalex.org/I158012942"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Heather M. Russell","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Richmond, Richmond, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Richmond, Richmond, USA","institution_ids":["https://openalex.org/I158012942"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5071847515"],"corresponding_institution_ids":["https://openalex.org/I16269868"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":1.4227,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.82086946,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"41","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9950000047683716,"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":0.9930999875068665,"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":0.7752073407173157},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7577474117279053},{"id":"https://openalex.org/keywords/edge-coloring","display_name":"Edge coloring","score":0.5150320529937744},{"id":"https://openalex.org/keywords/complete-coloring","display_name":"Complete coloring","score":0.4423704147338867},{"id":"https://openalex.org/keywords/greedy-coloring","display_name":"Greedy coloring","score":0.43405455350875854},{"id":"https://openalex.org/keywords/graph-coloring","display_name":"Graph coloring","score":0.42636871337890625},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3695412576198578},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.28696298599243164},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.06595703959465027},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.054302215576171875}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7752073407173157},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7577474117279053},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.5150320529937744},{"id":"https://openalex.org/C21642379","wikidata":"https://www.wikidata.org/wiki/Q3342988","display_name":"Complete coloring","level":5,"score":0.4423704147338867},{"id":"https://openalex.org/C38767284","wikidata":"https://www.wikidata.org/wiki/Q5601715","display_name":"Greedy coloring","level":5,"score":0.43405455350875854},{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.42636871337890625},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3695412576198578},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.28696298599243164},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.06595703959465027},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.054302215576171875}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00373-025-02938-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-025-02938-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-025-02938-1.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00373-025-02938-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-025-02938-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-025-02938-1.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320311294","display_name":"Santa Clara University","ror":"https://ror.org/03ypqe447"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4412364984.pdf","grobid_xml":"https://content.openalex.org/works/W4412364984.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W245060393","https://openalex.org/W1973079746","https://openalex.org/W1976445742","https://openalex.org/W1981764507","https://openalex.org/W2001124661","https://openalex.org/W2008263650","https://openalex.org/W2046344295","https://openalex.org/W2079887652","https://openalex.org/W2085554065","https://openalex.org/W2091208898","https://openalex.org/W2092653160","https://openalex.org/W2129794490","https://openalex.org/W2138261994","https://openalex.org/W2314361409","https://openalex.org/W2319873605","https://openalex.org/W2342698525","https://openalex.org/W2765516627","https://openalex.org/W2903114345","https://openalex.org/W2908677193","https://openalex.org/W2962755691","https://openalex.org/W3204791468","https://openalex.org/W4237496336","https://openalex.org/W4242643895","https://openalex.org/W4285619932","https://openalex.org/W4377819032","https://openalex.org/W4404822229"],"related_works":["https://openalex.org/W4291316360","https://openalex.org/W1542397451","https://openalex.org/W4311345810","https://openalex.org/W3169197204","https://openalex.org/W2380525562","https://openalex.org/W2585997002","https://openalex.org/W2385428710","https://openalex.org/W4229747356","https://openalex.org/W3177216142","https://openalex.org/W2365437454"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"chromatic":[2,85,137,196,214,219],"polynomial":[3,86,128,139,198,216,220],"$$\\pi":[4,88,140],"_{G}(k)$$":[5],"<mml:math":[6,41,90,142],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[7,42,91,143],"<mml:mrow>":[8,13,43,48,92,96,102,144,147,150,159],"<mml:msub>":[9,44,152],"<mml:mi>\u03c0</mml:mi>":[10,94,146],"<mml:mi>G</mml:mi>":[11,50,95,148],"</mml:msub>":[12,47,155],"<mml:mo>(</mml:mo>":[14,49,97,103,151,160],"<mml:mi>k</mml:mi>":[15,46,104,161],"<mml:mo>)</mml:mo>":[16,51,99,105,156,162],"</mml:mrow>":[17,18,52,53,100,106,107,149,157,163,164],"</mml:math>":[19,54,108,165],"of":[20,31,36,60,65,68,112,171,180,182,231],"a":[21,34,63,79,187,195],"graph":[22,236],"G":[23,61],"can":[24,75],"be":[25,76],"viewed":[26],"as":[27,62,78],"counting":[28,110],"the":[29,66,84,136,169,178,205,213,218],"number":[30,67,170,179],"vertices":[32],"in":[33,117,129,173,221],"family":[35],"coloring":[37,73,119,174],"graphs":[38,74],"$$\\mathcal":[39],"{C}_k(G)$$":[40],"<mml:mi>C</mml:mi>":[45],"associated":[55],"with":[56,228],"(proper)":[57],"k":[58,70,130],"-colorings":[59],"function":[64],"colors":[69],".":[71,131],"These":[72],"understood":[77],"reconfiguration":[80],"system.":[81],"We":[82,190,223],"generalize":[83],"to":[87,177,233],"_G^{(H)}(k)$$":[89],"<mml:msubsup>":[93,145],"<mml:mi>H</mml:mi>":[98],"</mml:msubsup>":[101,158],",":[109,166],"occurrences":[111],"arbitrary":[113],"induced":[114],"subgraphs":[115],"H":[116,232],"these":[118,125],"graphs,":[120,175],"and":[121,200,209],"we":[122,134,210],"prove":[123],"that":[124,184,212],"functions":[126],"are":[127],"In":[132],"particular,":[133],"study":[135],"pairs":[138,181,197,215],"_{G}^{(P_2)}(k)$$":[141],"<mml:mi>P</mml:mi>":[153],"<mml:mn>2</mml:mn>":[154],"which":[167],"counts":[168],"edges":[172],"corresponding":[176],"colorings":[183],"differ":[185],"on":[186],"single":[188],"vertex.":[189],"show":[191],"two":[192],"trees":[193],"share":[194],"if":[199,202],"only":[201],"they":[203],"have":[204],"same":[206],"degree":[207],"sequence,":[208],"conjecture":[211],"refines":[217],"general.":[222],"also":[224],"instantiate":[225],"our":[226],"polynomials":[227],"other":[229],"choices":[230],"generate":[234],"new":[235],"invariants.":[237]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}