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LIST EDGE AND LIST TOTAL COLORINGS OF PLANAR GRAPHS WITHOUT 6-CYCLES WITH CHORD

Guizhen Liu|Aijun Dong|Guojun Li
대한수학회 (The Korean Mathematical Society)|2012.03|대한수학회보 (Bulletin of the KMS)|제49권 제2호|pp. 359-365

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참고문헌

키워드

planar graphlist coloringchoosability
주제분류수학

초록

Giving a planar graph G, let $x^'_l(G)$ and $x^{''}_l(G)$ denote the list edge chromatic number and list total chromatic number of G respectively. It is proved that if a planar graph G without 6-cycles with chord, then $x^'_l(G){\leq}{\Delta}(G)+1$ and $x^{''}_l(G){\leq}{\Delta}(G)+2$ where ${\Delta}(G){\geq}6$.

Abstract

Giving a planar graph G, let $x^'_l(G)$ and $x^{''}_l(G)$ denote the list edge chromatic number and list total chromatic number of G respectively. It is proved that if a planar graph G without 6-cycles with chord, then $x^'_l(G){\leq}{\Delta}(G)+1$ and $x^{''}_l(G){\leq}{\Delta}(G)+2$ where ${\Delta}(G){\geq}6$.

참고문헌 (16)

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  11. T. Jensen, "Graph Coloring Problem" (1995), Wiley-Interscience
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