{"id":"https://openalex.org/W1583121507","doi":"https://doi.org/10.37236/1087","title":"Colorings and Orientations of Matrices and Graphs","display_name":"Colorings and Orientations of Matrices and Graphs","publication_year":2006,"publication_date":"2006-07-28","ids":{"openalex":"https://openalex.org/W1583121507","doi":"https://doi.org/10.37236/1087","mag":"1583121507"},"language":"en","primary_location":{"id":"doi:10.37236/1087","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1087","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r61/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r61/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029447093","display_name":"Uwe Schauz","orcid":"https://orcid.org/0000-0002-3116-9402"},"institutions":[{"id":"https://openalex.org/I8087733","display_name":"University of T\u00fcbingen","ror":"https://ror.org/03a1kwz48","country_code":"DE","type":"education","lineage":["https://openalex.org/I8087733"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Uwe Schauz","raw_affiliation_strings":["Department of Mathematics University Tbingen, Germany","Department of Mathematics University T\u00fcbingen, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics University Tbingen, Germany","institution_ids":["https://openalex.org/I8087733"]},{"raw_affiliation_string":"Department of Mathematics University T\u00fcbingen, Germany","institution_ids":["https://openalex.org/I8087733"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5029447093"],"corresponding_institution_ids":["https://openalex.org/I8087733"],"apc_list":null,"apc_paid":null,"fwci":1.0111,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.74981207,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"13","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9995999932289124,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9995999932289124,"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/T11476","display_name":"Graph theory and applications","score":0.9991999864578247,"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":0.9987000226974487,"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/mathematics","display_name":"Mathematics","score":0.8990559577941895},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8342106938362122},{"id":"https://openalex.org/keywords/eulerian-path","display_name":"Eulerian path","score":0.7170252203941345},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.669153094291687},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.6634426116943359},{"id":"https://openalex.org/keywords/greedy-coloring","display_name":"Greedy coloring","score":0.4423944056034088},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.44163280725479126},{"id":"https://openalex.org/keywords/list-coloring","display_name":"List coloring","score":0.4402925372123718},{"id":"https://openalex.org/keywords/graph-coloring","display_name":"Graph coloring","score":0.4207516014575958},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.41585391759872437},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4027926027774811},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.40167132019996643},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.13245424628257751},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.11615973711013794}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8990559577941895},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8342106938362122},{"id":"https://openalex.org/C43058520","wikidata":"https://www.wikidata.org/wiki/Q624580","display_name":"Eulerian path","level":3,"score":0.7170252203941345},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.669153094291687},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.6634426116943359},{"id":"https://openalex.org/C38767284","wikidata":"https://www.wikidata.org/wiki/Q5601715","display_name":"Greedy coloring","level":5,"score":0.4423944056034088},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.44163280725479126},{"id":"https://openalex.org/C199594403","wikidata":"https://www.wikidata.org/wiki/Q1130404","display_name":"List coloring","level":5,"score":0.4402925372123718},{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.4207516014575958},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.41585391759872437},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4027926027774811},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.40167132019996643},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.13245424628257751},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.11615973711013794},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/1087","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1087","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r61/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.86.7663","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.86.7663","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_13/PDF/v13i1r61.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1087","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1087","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r61/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1583121507.pdf","grobid_xml":"https://content.openalex.org/works/W1583121507.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W3297276","https://openalex.org/W345637930","https://openalex.org/W1568175246","https://openalex.org/W1970929688","https://openalex.org/W1972913697","https://openalex.org/W2067688212","https://openalex.org/W2072414205","https://openalex.org/W2148360835","https://openalex.org/W2911280162","https://openalex.org/W2914164509","https://openalex.org/W4299798129","https://openalex.org/W4301890399"],"related_works":["https://openalex.org/W4297911588","https://openalex.org/W4291316360","https://openalex.org/W2793500002","https://openalex.org/W2546620014","https://openalex.org/W1542397451","https://openalex.org/W4311345810","https://openalex.org/W3169197204","https://openalex.org/W2380525562","https://openalex.org/W4298054421","https://openalex.org/W1995859989"],"abstract_inverted_index":{"We":[0],"introduce":[1],"colorings":[2,37,98,107],"and":[3,51,57,72,81,88,108],"orientations":[4,34,56],"of":[5,9,17,21,38,45,60,66,76,96],"matrices":[6,44],"as":[7,28],"generalizations":[8],"the":[10,33,36,58,64,77,89,100],"graph":[11],"theoretic":[12],"terms.":[13],"The":[14,93],"permanent":[15],"per$(A[\\zeta|\\xi])$":[16],"certain":[18],"copies":[19],"$A[\\zeta|\\xi]$":[20],"a":[22,29],"matrix":[23,97,109],"$A$":[24],"can":[25],"be":[26],"expressed":[27],"weighted":[30],"sum":[31],"over":[32],"or":[35],"$A$.":[39],"When":[40],"applied":[41],"to":[42,105],"incidence":[43],"graphs":[46,68],"these":[47],"equations":[48],"include":[49],"Alon":[50],"Tarsi's":[52],"theorem":[53],"about":[54],"Eulerian":[55],"existence":[59],"list":[61,78],"colorings.":[62],"In":[63],"case":[65],"planar":[67],"we":[69],"deduce":[70],"Ellingham":[71],"Goddyn's":[73],"partial":[74],"solution":[75],"coloring":[79],"conjecture":[80],"Scheim's":[82],"equivalency":[83],"between":[84],"not":[85],"vanishing":[86],"permanents":[87],"four":[90],"color":[91],"theorem.":[92],"general":[94],"concept":[95],"in":[99],"background":[101],"is":[102],"also":[103],"connected":[104],"hypergraph":[106],"choosability.":[110]},"counts_by_year":[{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
