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SOME RESULTS ON TOTAL COLORINGS OF PLANAR GRAPHS
Hou, Jianfeng,Liu, Guizhen,Xin, Yongxun,Lan, Mei Korean Society of Computational and Applied Mathem 2008 Journal of applied mathematics & informatics Vol.26 No.3-4
Let G be a planar graph. It is proved that if G does not contain a k-cycle with a chord for some k ${\ni}$ {4,5,6}, then G is total-($\Delta(G)+2$)-colorable.
Some results on total colorings of planar graphs
Jianfeng Hou,Guizhen Liu,Yongxun Xin,Mei Lan 한국전산응용수학회 2008 Journal of applied mathematics & informatics Vol.26 No.3-4
Let G be a planar graph. It is proved that if G does not contain a k-cycle with a chord for some k ∈ {4, 5, 6}, then G is total-(△(G) + 2)-colorable.