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A strong edge coloring of a graph G is a proper edge coloring in which every color class is an induced matching. The strong chromatic index χs(G) of a graph G is the minimum number of colors in a strong edge coloring of G. In this note, we improve a result by Dębski et al. [Strong chromatic index of sparse graphs, arXiv:1301.1992v1] and show that the strong chromatic index of a k-degenerate gra...

A twin edge k-coloring of a graph G is a proper edge k-coloring of G with the elements of Zk so that the induced vertex k-coloring, in which the color of a vertex v in G is the sum in Zk of the colors of the edges incident with v, is a proper vertex k-coloring. The minimum k for which G has a twin edge k-coloring is called the twin chromatic index of G. Twin chromatic index of the square P 2 n ...

A strong edge-coloring of a graph G is a function that assigns to each edge a color such that two edges within distance two apart must receive different colors. The minimum number of colors used in a strong edge-coloring is the strong chromatic index of G. Lih and Liu [14] proved that the strong chromatic index of a cubic Halin graph, other than two special graphs, is 6 or 7. It remains an open...

Let G = (V, E) be a graph and k > 2 an integer. The general chromatic index x;(G) of G is the minimum order of a partition P of E such that for any set F in P every component in the subgraph (F) induced by F has size at most k1. This paper initiates a study of x;(G) and generalizes some known results on chromatic index. The purpose of this paper is to obtain a generalization of chromatic index....

Given a graph G, an automorphic edge(vertex)-coloring of G is a proper edge(vertex)-coloring such that each automorphism of the graph preserves the coloring. The automorphic chromatic index (number) is the least integer k for which G admits an automorphic edge(vertex)coloring with k colors. We show that it is NP-complete to determine the automorphic chromatic index and the automorphic chromatic...

We present an improved upper bound of O(d 1 m−1 ) for the (2,F)-subgraph chromatic number χ2,F (G) of any graph G of maximum degree d. Here, m denotes the minimum number of edges in any member of F . This bound is tight up to a (log d) multiplicative factor and improves the previous bound presented in [1]. We also obtain a relationship connecting the oriented chromatic number χo(G) of graphs an...