Decompositions for edge-coloring join graphs and cobipartite graphs

作者：Machado Raphael C S^*; de Figueiredo Celina M N

来源：Discrete Applied Mathematics, 2010, 158(12): 1336-1342.

DOI：10.1016/j.dam.2009.01.009

• Edge-coloring
• Chromatic index
• Join graph
• Cobipartite graph
• Core

An edge-coloring is an association of colors to the edges of a graph, in such a way that no pair of adjacent edges receive the same color. A graph G is Class 1 if it is edge-colorable with a number of colors equal to its maximum degree Delta(G). To determine whether a graph G is Class 1 is NP-complete [I. Holyer, The NP-completeness of edge-coloring, SIAM J. Comput. 10 (1981) 718-720]. First, we propose edge-decompositions of a graph G with the goal of edge-coloring G with Delta(G) colors. Second, we apply these decompositions for identifying new subsets of Class I join graphs and cobipartite graphs. Third, the proposed technique is applied for proving that the chromatic index of a graph is equal to the chromatic index of its semi-core, the subgraph induced by the maximum degree vertices and their neighbors. Finally, we apply these decomposition tools to a classical result [A.J.W. Hilton, Z. Cheng, The chromatic index of a graph whose core has maximum degree 2, Discrete Math. 101 (1992) 135-147] that relates the chromatic index of a graph to its core, the subgraph induced by the maximum degree vertices.

• 出版日期2010-6-28