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New Results on Chromatic Index Critical Graphs

XU Ji-ju

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Abstract

The chromatic index X'(G) of a graph G is the minimun number of colors required to color the edges of G so that two adjacent edges receive different colors.In 1965,Vizing proved that if G is a graph of maximun degree △,then X'(G) is either △ or △ + 1.If G is a connected graph and X'(G-e) X'(G) exists in every edge(e) of G,it can be called a critical graph.In this paper,we prove several new results on chromatic index critical graphs.We also give a new upper bound on the size of chromatic index critical graphs of even order.

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The chromatic index X'(G) of a graph G is the minimun number of colors required to color the edges of G so that two adjacent edges receive different colors.In 1965,Vizing proved that if G is a graph of maximun degree △,then X'(G) is either △ or △ + 1.If G is a connected graph and X'(G-e) X'(G) exists in every edge(e) of G,it can be called a critical graph.In this paper,we prove several new results on chromatic index critical graphs.We also give a new upper bound on the size of chromatic index critical graphs of even order.

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Available abstract

The chromatic index X'(G) of a graph G is the minimun number of colors required to color the edges of G so that two adjacent edges receive different colors.In 1965,Vizing proved that if G is a graph of maximun degree △,then X'(G) is either △ or △ + 1.If G is a connected graph and X'(G-e) X'(G) exists in every edge(e) of G,it can be called a critical graph.In this paper,we prove several new results on chromatic index critical graphs.We also give a new upper bound on the size of chromatic index critical graphs of even order.

Key concepts: Edge coloring, Critical graph, Combinatorics, Chromatic scale, Graph, Mathematics, Connectivity, Friendship graph

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