Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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LIST EDGE AND LIST TOTAL COLORINGS OF PLANAR GRAPHS WITHOUT 6-CYCLES WITH CHORD

  • Dong, Aijun (School of Mathematics Shandong University) ;
  • Liu, Guizhen (School of Mathematics Shandong University) ;
  • Li, Guojun (School of Mathematics Shandong University)
  • Received : 2010.11.05
  • Published : 2012.03.31
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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 ${\Delta}(G){\geq}6$.

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References

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