{"id":"https://openalex.org/W1977197609","doi":"https://doi.org/10.1137/080736697","title":"A New Proof of the <i>H</i>-Coloring Dichotomy","display_name":"A New Proof of the <i>H</i>-Coloring Dichotomy","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W1977197609","doi":"https://doi.org/10.1137/080736697","mag":"1977197609"},"language":"en","primary_location":{"id":"doi:10.1137/080736697","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080736697","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/A5068721384","display_name":"Mark Siggers","orcid":"https://orcid.org/0000-0001-7070-9021"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mark H. Siggers","raw_affiliation_strings":["mhsiggers@knu.ac.kr#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"mhsiggers@knu.ac.kr#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5068721384"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1033,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.74201474,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"23","issue":"4","first_page":"2204","last_page":"2210"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9973000288009644,"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"}},"topics":[{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9973000288009644,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9932000041007996,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9930999875068665,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/mathematics","display_name":"Mathematics","score":0.7906148433685303},{"id":"https://openalex.org/keywords/proof-complexity","display_name":"Proof complexity","score":0.6726579070091248},{"id":"https://openalex.org/keywords/combinatorial-proof","display_name":"Combinatorial proof","score":0.6715732216835022},{"id":"https://openalex.org/keywords/direct-proof","display_name":"Direct proof","score":0.5462193489074707},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5276766419410706},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4984414577484131},{"id":"https://openalex.org/keywords/analytic-proof","display_name":"Analytic proof","score":0.49163752794265747},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4903245270252228},{"id":"https://openalex.org/keywords/structural-proof-theory","display_name":"Structural proof theory","score":0.47977811098098755},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.4491250514984131},{"id":"https://openalex.org/keywords/proof-of-concept","display_name":"Proof of concept","score":0.43228408694267273},{"id":"https://openalex.org/keywords/proof-theory","display_name":"Proof theory","score":0.41859108209609985},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12107247114181519}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7906148433685303},{"id":"https://openalex.org/C105605280","wikidata":"https://www.wikidata.org/wiki/Q7249999","display_name":"Proof complexity","level":3,"score":0.6726579070091248},{"id":"https://openalex.org/C118539577","wikidata":"https://www.wikidata.org/wiki/Q3402784","display_name":"Combinatorial proof","level":2,"score":0.6715732216835022},{"id":"https://openalex.org/C161505775","wikidata":"https://www.wikidata.org/wiki/Q3240280","display_name":"Direct proof","level":2,"score":0.5462193489074707},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5276766419410706},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4984414577484131},{"id":"https://openalex.org/C135754263","wikidata":"https://www.wikidata.org/wiki/Q4751136","display_name":"Analytic proof","level":3,"score":0.49163752794265747},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4903245270252228},{"id":"https://openalex.org/C195653647","wikidata":"https://www.wikidata.org/wiki/Q7625047","display_name":"Structural proof theory","level":4,"score":0.47977811098098755},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.4491250514984131},{"id":"https://openalex.org/C124978682","wikidata":"https://www.wikidata.org/wiki/Q1201019","display_name":"Proof of concept","level":2,"score":0.43228408694267273},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.41859108209609985},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12107247114181519},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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:10.1137/080736697","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080736697","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":7,"referenced_works":["https://openalex.org/W655258421","https://openalex.org/W1975452925","https://openalex.org/W1984264511","https://openalex.org/W2017724352","https://openalex.org/W2025319967","https://openalex.org/W2026753685","https://openalex.org/W2077575555"],"related_works":["https://openalex.org/W2922318846","https://openalex.org/W171706349","https://openalex.org/W4234403895","https://openalex.org/W2461509449","https://openalex.org/W3173957725","https://openalex.org/W3157478331","https://openalex.org/W187835144","https://openalex.org/W2626436722","https://openalex.org/W153148314","https://openalex.org/W2736121670"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"present":[4],"a":[5],"new":[6],"proof":[7,31,38],"of":[8,44],"the":[9,36,41],"H-coloring":[10],"dichotomy,":[11],"which":[12],"was":[13,24],"first":[14],"proved":[15],"by":[16,26],"Hell":[17],"and":[18,22,39],"Ne\u0161et\u0159il":[19],"in":[20,28],"1990,":[21],"then":[23],"reproved":[25],"Bulatov":[27],"2005.":[29],"Our":[30],"is":[32],"much":[33],"shorter":[34],"than":[35],"original":[37],"avoids":[40],"algebraic":[42],"machinery":[43],"Bulatov's":[45],"proof.":[46]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}