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ENTIRE CHROMATIC NUMBER AND Δ-MATCHING OF OUTERPLANE GRAPHS
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作者 王维凡 张克民 《Acta Mathematica Scientia》 SCIE CSCD 2005年第4期672-680,共9页
Let G be an outerplane graph with maximum degree A and the entire chromatic number Xvef(G). This paper proves that if △ ≥6, then △+ 1≤Xvef(G)≤△+ 2, and Xvef (G) = △+ 1 if and only if G has a matching M... Let G be an outerplane graph with maximum degree A and the entire chromatic number Xvef(G). This paper proves that if △ ≥6, then △+ 1≤Xvef(G)≤△+ 2, and Xvef (G) = △+ 1 if and only if G has a matching M consisting of some inner edges which covers all its vertices of maximum degree. 展开更多
关键词 Outerplane graph MATCHING entire chromatic number
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The Entire Coloring of Series-Parallel Graphs 被引量:4
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作者 Jian-liangWu Yu-liangWu 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2005年第1期61-66,共6页
The entire chromatic number χ_(vef) (G) of a plane graph G is the minimalnumber of colors needed for coloring vertices, edges and faces of G such that no two adjacent orincident elements are of the same color. Let G ... The entire chromatic number χ_(vef) (G) of a plane graph G is the minimalnumber of colors needed for coloring vertices, edges and faces of G such that no two adjacent orincident elements are of the same color. Let G be a series-parallel plane graph, that is, a planegraph which contains no subgraphs homeomorphic to K 4. It is proved in this paper that χ_(vef)(G)≤ max{8, Δ(G) + 2} and χ_(vef) (G) = Δ + 1 if G is 2-connected and Δ(G) ≥ 6. 展开更多
关键词 series-parallel graph the entire coloring the entire chromatic number
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