{"id":{"repo_id":"wvu","oai_identifier":"oai:researchrepository.wvu.edu:etd-2605"},"canonical_url":"https://search.dev.ndltd.org/etd/wvu/oai:researchrepository.wvu.edu:etd-2605","repository":{"repo_id":"wvu","name":"West Virginia University","base_url":"https://researchrepository.wvu.edu/do/oai/"},"display":{"title":"Edge coloring of simple graphs and edge -face coloring of simple plane graphs","abstract":"We prove that chie( G) = Delta if Delta ≥ 5 and g ≥ 4, or Delta ≥ 4 and g ≥ 5, or Delta ≥ 3 and g ≥ 9. In addition, if chi(Sigma) > 0, then chie( G) = Delta if Delta ≥ 3 and g ≥ 8 where Delta, g is the maximum degree, the girth of the graph G, respectively.;It is proved that G is not critical if d¯ ≤ 6 and Delta ≥ 8, or d¯ ≤ 203 and Delta ≥ 9. This result generalizes earlier results.;Given a simple plane graph G, an edge-face k-coloring of G is a function &phis; : E(G) ∪ F(G) {lcub}1, ···, k{rcub} such that, for any two adjacent elements a, b ∈ E(G) ∪ F(G), &phis;( a) ≠ &phis;(b). Denote chie( G), chief(G), Delta( G) the edge chromatic number, the edge-face chromatic number and the maximum degree of G, respectively. We prove that chi ef(G) = chie( G) = Delta(G) for any 2-connected simple plane graph G with Delta(G) ≥ 24.","abstract_html":"We prove that chie( G) = Delta if Delta ≥ 5 and g ≥ 4, or Delta ≥ 4 and g ≥ 5, or Delta ≥ 3 and g ≥ 9. In addition, if chi(Sigma) > 0, then chie( G) = Delta if Delta ≥ 3 and g ≥ 8 where Delta, g is the maximum degree, the girth of the graph G, respectively.;It is proved that G is not critical if d¯ ≤ 6 and Delta ≥ 8, or d¯ ≤ 203 and Delta ≥ 9. This result generalizes earlier results.;Given a simple plane graph G, an edge-face k-coloring of G is a function &phis; : E(G) ∪ F(G) {lcub}1, ···, k{rcub} such that, for any two adjacent elements a, b ∈ E(G) ∪ F(G), &phis;( a) ≠ &phis;(b). Denote chie( G), chief(G), Delta( G) the edge chromatic number, the edge-face chromatic number and the maximum degree of G, respectively. We prove that chi ef(G) = chie( G) = Delta(G) for any 2-connected simple plane graph G with Delta(G) ≥ 24.","abstract_has_math":false,"creators":["Luo, Rong"],"institution":null,"degree_name":"PhD","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Cun-Quan Zhang."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2002,"date_issued":"2002-05-01T07:00:00Z","date_published":"2002-05-01T07:00:00Z","updated_at":"2026-07-24T06:15:55Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://researchrepository.wvu.edu/etd/1602"],"render_values":[{"text":"https://researchrepository.wvu.edu/etd/1602","href":"https://researchrepository.wvu.edu/etd/1602","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.33915/etd.1602","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Cun-Quan Zhang."]},{"key":"dc:creator","label":"Author","values":["Luo, Rong"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2019-01-17T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["PhD"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://doi.org/10.33915/etd.1602","https://researchrepository.wvu.edu/etd/1602"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We prove that chie( G) = Delta if Delta ≥ 5 and g ≥ 4, or Delta ≥ 4 and g ≥ 5, or Delta ≥ 3 and g ≥ 9. In addition, if chi(Sigma) > 0, then chie( G) = Delta if Delta ≥ 3 and g ≥ 8 where Delta, g is the maximum degree, the girth of the graph G, respectively.;It is proved that G is not critical if d¯ ≤ 6 and Delta ≥ 8, or d¯ ≤ 203 and Delta ≥ 9. This result generalizes earlier results.;Given a simple plane graph G, an edge-face k-coloring of G is a function &phis; : E(G) ∪ F(G) {lcub}1, ···, k{rcub} such that, for any two adjacent elements a, b ∈ E(G) ∪ F(G), &phis;( a) ≠ &phis;(b). Denote chie( G), chief(G), Delta( G) the edge chromatic number, the edge-face chromatic number and the maximum degree of G, respectively. We prove that chi ef(G) = chie( G) = Delta(G) for any 2-connected simple plane graph G with Delta(G) ≥ 24."]},{"key":"dc:title","label":"Title","values":["Edge coloring of simple graphs and edge -face coloring of simple plane graphs"]}]}],"canonical_facts":{"dc:contributor":["Cun-Quan Zhang."],"dc:creator":["Luo, Rong"],"dc:date.available":["2019-01-17T08:00:00Z"],"dc:description.abstract":["We prove that chie( G) = Delta if Delta ≥ 5 and g ≥ 4, or Delta ≥ 4 and g ≥ 5, or Delta ≥ 3 and g ≥ 9. In addition, if chi(Sigma) > 0, then chie( G) = Delta if Delta ≥ 3 and g ≥ 8 where Delta, g is the maximum degree, the girth of the graph G, respectively.;It is proved that G is not critical if d¯ ≤ 6 and Delta ≥ 8, or d¯ ≤ 203 and Delta ≥ 9. This result generalizes earlier results.;Given a simple plane graph G, an edge-face k-coloring of G is a function &phis; : E(G) ∪ F(G) {lcub}1, ···, k{rcub} such that, for any two adjacent elements a, b ∈ E(G) ∪ F(G), &phis;( a) ≠ &phis;(b). Denote chie( G), chief(G), Delta( G) the edge chromatic number, the edge-face chromatic number and the maximum degree of G, respectively. We prove that chi ef(G) = chie( G) = Delta(G) for any 2-connected simple plane graph G with Delta(G) ≥ 24."],"dc:identifier":["https://doi.org/10.33915/etd.1602","https://researchrepository.wvu.edu/etd/1602"],"dc:subject":["Mathematics"],"dc:title":["Edge coloring of simple graphs and edge -face coloring of simple plane graphs"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["PhD"]},"updated_at":"2026-07-24T06:15:55Z"}