An edge-coloring of a graph G with colors 1, 2, . . . , t is an interval t-coloring if all colors are used, and the colors of edges incident to each vertex of G are distinct and form an interval of integers. A graph G is interval colorable if it has an interval t-coloring for some positive integer t. For an interval colorable graph G, W (G) denotes the greatest value of t for which G has an int...

Abs t r ac t . In an edge-coloring of a graph G = (V, E) each color appears around each vertex at most once. An f-coloring is a generalization of an edge-coloring in which each color appears around each vertex v at most f(v) times where f is a function assigning a natural number f(v) e N to each vertex v E V. In this paper we first give a simple reduction of the f-coloring problem to the ordina...

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...

A k-edge-coloring of a graph G = (V, E) is a function c that assigns an integer c(e) (called color) in {0, 1, · · · , k−1} to every edge e ∈ E so that adjacent edges get different colors. A k-edge-coloring is linear compact if the colors incident to every vertex are consecutive. The problem k − LCCP is to determine whether a given graph admits a linear compact k-edge coloring. A k-edge-coloring...

If c : E → {1, 2, . . . , k} is a proper edge coloring of a graph G = (V,E) then the palette S(v) of a vertex v ∈ V is the set of colors of the incident edges: S(v) = {c(e) : e = vw ∈ E}. An edge coloring c distinguishes vertices u and v if S(u) 6= S(v). A d-strong edge coloring of G is a proper edge coloring that distinguishes all pairs of vertices u and v with distance d(u, v) ≤ d. The minimu...

We prove that the list chromatic index of a graph of maximum degree and treewidth ≤ √2 − 3 is ; and that the total chromatic number of a graph of maximum degree and treewidth ≤ /3 + 1 is + 1. This improves results by Meeks and Scott. C © 2015 Wiley Periodicals, Inc. J. Graph Theory 81: 272–282, 2016

We prove that the list chromatic index of a graph of maximum degree ∆ and treewidth ≤ √ 2∆ − 3 is ∆; and that the total chromatic number of a graph of maximum degree ∆ and treewidth ≤ ∆/3 + 1 is ∆ + 1. This improves results by Meeks and Scott.

In this paper, we aim to introduce the group version of edge coloring and list edge coloring, and prove that all 2-degenerate graphs along with some planar graphs without adjacent short cycles is group (∆(G) + 1)-edgechoosable while some planar graphs with large girth and maximum degree is group ∆(G)-edge-choosable.

A facial parity edge coloring of a 2-edge-connected plane graph is such an edge coloring in which no two face-adjacent edges (consecutive edges of a facial walk of some face) receive the same color, in addition, for each face f and each color c, either no edge or an odd number of edges incident with f is colored with c. It is known that any 2-edgeconnected plane graph has a facial parity edge c...

Abstract. A skew edge coloring of a graph G is defined to be a set of two edge colorings such that no two edges are assigned the same unordered pair of colors. The skew chromatic index s(G) is the minimum number of colors required for a skew edge coloring of G. In this paper, an algorithm is determined for skew edge coloring of circular ladder graphs. Alsothe skew chromatic index of circular la...