{"id":"https://openalex.org/W1975406723","doi":"https://doi.org/10.1137/070687988","title":"Edge-Face Total Chromatic Number of Halin Graphs","display_name":"Edge-Face Total Chromatic Number of Halin Graphs","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W1975406723","doi":"https://doi.org/10.1137/070687988","mag":"1975406723"},"language":"en","primary_location":{"id":"doi:10.1137/070687988","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070687988","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/A5101976336","display_name":"Wai Hong Chan","orcid":"https://orcid.org/0000-0002-6614-3501"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"W. H. Chan","raw_affiliation_strings":["dchan@hkbu.edu.hk and cblam@yahoo.com and wcshiu@hkbu.edu.hk#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"dchan@hkbu.edu.hk and cblam@yahoo.com and wcshiu@hkbu.edu.hk#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111722096","display_name":"Peter Che Bor Lam","orcid":null},"institutions":[{"id":"https://openalex.org/I141568987","display_name":"Hong Kong Baptist University","ror":"https://ror.org/0145fw131","country_code":"HK","type":"education","lineage":["https://openalex.org/I141568987"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Peter C. B. Lam","raw_affiliation_strings":["Hong Kong Baptist University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hong Kong Baptist University","institution_ids":["https://openalex.org/I141568987"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076646903","display_name":"Wai Chee Shiu","orcid":"https://orcid.org/0000-0002-2819-8480"},"institutions":[{"id":"https://openalex.org/I530967","display_name":"Toronto Metropolitan University","ror":"https://ror.org/05g13zd79","country_code":"CA","type":"education","lineage":["https://openalex.org/I530967"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"W. C. Shiu","raw_affiliation_strings":["Department of Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics","institution_ids":["https://openalex.org/I530967"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3545,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.5957455,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"23","issue":"3","first_page":"1646","last_page":"1654"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9937000274658203,"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":0.9937000274658203,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9746999740600586,"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/T12401","display_name":"Scheduling and Timetabling Solutions","score":0.9214000105857849,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8550633192062378},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8412425518035889},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.5791054368019104},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.527515709400177},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4781128764152527},{"id":"https://openalex.org/keywords/face","display_name":"Face (sociological concept)","score":0.4568212628364563},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.43708494305610657},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4281194508075714},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09581363201141357},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06768175959587097}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8550633192062378},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8412425518035889},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.5791054368019104},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.527515709400177},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4781128764152527},{"id":"https://openalex.org/C2779304628","wikidata":"https://www.wikidata.org/wiki/Q3503480","display_name":"Face (sociological concept)","level":2,"score":0.4568212628364563},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.43708494305610657},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4281194508075714},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09581363201141357},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06768175959587097},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C36289849","wikidata":"https://www.wikidata.org/wiki/Q34749","display_name":"Social science","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/070687988","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070687988","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"},{"id":"pmh:oai:repository.hkbu.edu.hk:hkbu_staff_publication-1982","is_oa":false,"landing_page_url":"https://repository.hkbu.edu.hk/hkbu_staff_publication/968","pdf_url":null,"source":{"id":"https://openalex.org/S4377196872","display_name":"HKBU Institutional Repository (Hong Kong Baptist University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I141568987","host_organization_name":"Hong Kong Baptist University","host_organization_lineage":["https://openalex.org/I141568987"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"HKBU Staff Publication","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W2018432434"],"related_works":["https://openalex.org/W2181667894","https://openalex.org/W2105223880","https://openalex.org/W2379048343","https://openalex.org/W2148696453","https://openalex.org/W4256403421","https://openalex.org/W2062039730","https://openalex.org/W2074120492","https://openalex.org/W2152117225","https://openalex.org/W2950817880","https://openalex.org/W3178681420"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2],"the":[3,25],"edge-face":[4],"total":[5,36],"chromatic":[6],"number":[7],"of":[8,27],"Halin":[9],"graphs":[10],"with":[11],"maximum":[12],"vertex":[13],"degree":[14],"$\\Delta$":[15],"not":[16],"less":[17],"than":[18],"4":[19],"is":[20],"equal":[21],"to":[22],"$\\max\\{5,\\Delta\\}$.":[23],"For":[24],"cases":[26],"$\\Delta=4$":[28],"and":[29],"5,":[30],"we":[31],"provide":[32],"a":[33],"proper":[34],"5-edge-face":[35],"coloring":[37],"algorithm.":[38]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}