Work

On star edge colorings of bipartite and subcubic graphs

Year: 2021

Type: article

Abstract: A star edge coloring of a graph is a proper edge coloring with no 2-colored path or cycle of length four. The star chromatic index χst′(G) of G is the minimum number t for which G has a star edge coloring with t colors. We prove upper bounds for the star chromatic index of bipartite graphs G where all vertices in one part have maximum degree 2 and all vertices in the other part has maximum degree b. Let k be an integer (k≥1); we prove that if b=2k+1, then χst′(G)≤3k+2; and if b=2k, then χst′(G)≤3k; both upper bounds are sharp. We also consider complete bipartite graphs; in particular we determine the star chromatic index of such graphs when one part has size at most 3, and prove upper bounds for the general case. Finally, we consider the well-known conjecture that subcubic graphs have star chromatic index at most 6; in particular we settle this conjecture for cubic Halin graphs.

Source: Discrete Applied Mathematics

DOI: 10.1016/j.dam.2021.03.007

Authors: Carl Johan Casselgren, Jonas B. Granholm, André Raspaud

Institutions: Linköping University, Université de Bordeaux, Laboratoire Bordelais de Recherche en Informatique

Language: English

Topic: Graph Labeling and Dimension Problems

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,590

Funders: Agence Nationale de la Recherche, Vetenskapsrådet