The circular chromatic index of some class 2 graphs

Skew Chromatic Index of Circular Ladder Graphs

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...

The circular chromatic index of graphs of high girth

We show that for each ε > 0 and each integer ∆ ≥ 1, there exists a number g such that for any graph G of maximum degree ∆ and girth at least g, the circular chromatic index of G is at most ∆ + ε.

The circular chromatic index

Circular chromatic index of Cartesian products of graphs

The circular chromatic index of a graph G, written χ′c(G), is the minimum r permitting a function f : E(G) → [0, r) such that 1 ≤ |f(e)− f(e)| ≤ r − 1 whenever e and e are incident. Let G = H2C2m+1, where 2 denotes Cartesian product and H is an (s − 2)-regular graph of odd order, with s ≡ 0 mod 4 (thus G is sregular). We prove that χ′c(G) ≥ s+ ⌊λ(1− 1/s)⌋ , where λ is the minimum, over all base...

The strong chromatic index of a class of graphs

The strong chromatic index of a graph G is the minimum integer k such that the edge set of G can be partitioned into k induced matchings. Faudree et al. [R.J. Faudree, R.H. Schelp, A. Gyárfás, Zs. Tuza, The strong chromatic index of graphs, Ars Combin. 29B (1990) 205–211] proposed an open problem: If G is bipartite and if for each edge xy ∈ E(G), d(x)+ d(y) ≤ 5, then sχ (G) ≤ 6. Let H0 be the g...