Parsimonious edge coloring

Abstract In a graph G of maximum degree Δ, let γ denote the largest fraction of edges that can be Δ-edge-colored. This paper investigates lower bounds for γ together with infinite families of graphs in which γ is bounded away from 1. For instance, if G is cubic, then γ ⩾ 13 15 ; and there exists an infinite family of 3-connected cubic graphs in which γ ⩽ 25 27 .

[1]  G. A. Dirac,et al.  Short Proof of a Map-Colour Theorem , 1957, Canadian Journal of Mathematics.

[2]  Frank Harary,et al.  Graph Theory , 2016 .

[3]  C. Thomassen,et al.  Five-Coloring Maps on Surfaces , 1993, J. Comb. Theory, Ser. B.

[4]  William Staton,et al.  Extremal bipartite subgraphs of cubic triangle-free graphs , 1982, J. Graph Theory.

[5]  Paul Seymour,et al.  On Tutte's extension of the four-colour problem , 1981, J. Comb. Theory, Ser. B.

[6]  S. C. Locke.  Maximum k-colorable subgraphs , 1982, J. Graph Theory.

[7]  S. C. Locke,et al.  Largest bipartite subgraphs in triangle-free graphs with maximum degree three , 1986 .