Edge colorings of planar graphs with maximum degree five

Journal of East China Normal University(Natural Sc ›› 2011, Vol. 2011 ›› Issue (2): 32-38.

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Edge colorings of planar graphs with maximum degree five

NI Wei-ping

Department of Mathematics and Information Science, aozhuang University，Zaozhuang Shandong 277160, China

Received:2009-11-01 Revised:2010-02-01 Online:2011-03-25 Published:2011-03-25
Contact: NI Wei-ping

Abstract

Abstract: By applying a discharging method and using some theorems of critical graphs, we proved that every planar graph G with Δ=5 is of class 1, if any 3-cycle is not adjacent to any 4-cycle or to any 5-cycle in G. Therefore, we concluded two sufficient conditions for planar graph G to be Class 1.

Key words: edge coloring, maximum degree, cycle, planar graph, edge coloring, maximum degree, cycle

CLC Number:

O157.5

NI Wei-ping. Edge colorings of planar graphs with maximum degree five[J]. Journal of East China Normal University(Natural Sc, 2011, 2011(2): 32-38.

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Edge colorings of planar graphs with maximum degree five

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