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2013•Journal of Zhengzhou UniversityRequires access

A Construction of Chromatic Index Critical Graphs of Maximum Degree 3

Shi Wen-jun

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Abstract

The chromatic index χ′(G) of a graph G was the minimum number of colors required to color the edges of G so that different colors were received for two adjacent edges.Five quadrangle extension types of graphs of maximum degree 3 were given and the stable criticality of them was proved.Furthermore,it could be used to construct new critical graphs in higher color levels.

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The chromatic index χ′(G) of a graph G was the minimum number of colors required to color the edges of G so that different colors were received for two adjacent edges.Five quadrangle extension types of graphs of maximum degree 3 were given and the stable criticality of them was proved.Furthermore,it could be used to construct new critical graphs in higher color levels.

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Available abstract

The chromatic index χ′(G) of a graph G was the minimum number of colors required to color the edges of G so that different colors were received for two adjacent edges.Five quadrangle extension types of graphs of maximum degree 3 were given and the stable criticality of them was proved.Furthermore,it could be used to construct new critical graphs in higher color levels.

Key concepts: Edge coloring, Mathematics, Degree (music), Graph, Quadrangle, Chromatic scale, Extension (predicate logic), Brooks' theorem

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