{"id":"https://openalex.org/W2033457765","doi":"https://doi.org/10.1016/0012-365x(73)90168-4","title":"Graphs with valency k, edge connectivity k, chromatic index k + 1 and arbitrary girth","display_name":"Graphs with valency k, edge connectivity k, chromatic index k + 1 and arbitrary girth","publication_year":1973,"publication_date":"1973-04-01","ids":{"openalex":"https://openalex.org/W2033457765","doi":"https://doi.org/10.1016/0012-365x(73)90168-4","mag":"2033457765"},"language":"en","primary_location":{"id":"doi:10.1016/0012-365x(73)90168-4","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0012-365x(73)90168-4","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"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/A5046440641","display_name":"Vance Faber","orcid":"https://orcid.org/0000-0001-5125-6979"},"institutions":[{"id":"https://openalex.org/I921990950","display_name":"University of Colorado Denver","ror":"https://ror.org/02hh7en24","country_code":"US","type":"education","lineage":["https://openalex.org/I921990950"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"V. Faber","raw_affiliation_strings":["University of Colorado, Denver Center, Colo. 80202, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"University of Colorado, Denver Center, Colo. 80202, USA#TAB#","institution_ids":["https://openalex.org/I921990950"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086429144","display_name":"Jerzy Mycielski","orcid":"https://orcid.org/0000-0003-4874-030X"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. Mycielski","raw_affiliation_strings":["University of Colorado, Boulder, Colo. 80302, USA\u2020\u2020"],"affiliations":[{"raw_affiliation_string":"University of Colorado, Boulder, Colo. 80302, USA\u2020\u2020","institution_ids":["https://openalex.org/I188538660"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5046440641"],"corresponding_institution_ids":["https://openalex.org/I921990950"],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.19348518,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"4","issue":"4","first_page":"339","last_page":"345"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9994000196456909,"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":0.9994000196456909,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9962999820709229,"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":0.9912999868392944,"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/valency","display_name":"Valency","score":0.9113942384719849},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8641090393066406},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7175157070159912},{"id":"https://openalex.org/keywords/girth","display_name":"Girth (graph theory)","score":0.6893674731254578},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.5689669251441956},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.553370475769043},{"id":"https://openalex.org/keywords/edge-coloring","display_name":"Edge coloring","score":0.5343564748764038},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5291476845741272},{"id":"https://openalex.org/keywords/index","display_name":"Index (typography)","score":0.4223073422908783},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.32801002264022827},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07110300660133362},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.05843043327331543},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.04892203211784363}],"concepts":[{"id":"https://openalex.org/C139007053","wikidata":"https://www.wikidata.org/wiki/Q1412952","display_name":"Valency","level":2,"score":0.9113942384719849},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8641090393066406},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7175157070159912},{"id":"https://openalex.org/C2777434295","wikidata":"https://www.wikidata.org/wiki/Q959831","display_name":"Girth (graph theory)","level":2,"score":0.6893674731254578},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.5689669251441956},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.553370475769043},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.5343564748764038},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5291476845741272},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.4223073422908783},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.32801002264022827},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07110300660133362},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.05843043327331543},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.04892203211784363},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0012-365x(73)90168-4","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0012-365x(73)90168-4","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W181968519","https://openalex.org/W1482143660","https://openalex.org/W1504925519","https://openalex.org/W1518358948","https://openalex.org/W1975328965","https://openalex.org/W2016461386","https://openalex.org/W2019284393","https://openalex.org/W2146117644","https://openalex.org/W2506153394","https://openalex.org/W2799004609","https://openalex.org/W4233249038","https://openalex.org/W4245236715","https://openalex.org/W6607512994","https://openalex.org/W6630069087"],"related_works":["https://openalex.org/W2762663192","https://openalex.org/W1992814711","https://openalex.org/W431658849","https://openalex.org/W1998523619","https://openalex.org/W638739646","https://openalex.org/W4212917371","https://openalex.org/W1979918629","https://openalex.org/W2171451941","https://openalex.org/W1575653887","https://openalex.org/W2237219011"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
