TY - JOUR
T1 - Injective edge-coloring of graphs with given maximum degree
AU - Kostochka, Alexandr
AU - Raspaud, André
AU - Xu, Jingwei
N1 - Funding Information:
Partially supported by NSF, USA grant DMS-1600592, NSF RTG, USA Grant DMS-1937241, ANR, France project HOSIGRA (ANR-17-CE40-0022) and grant 19-01-00682 of the Russian Foundation for Basic Research.This work is supported by the ANR, France project HOSIGRA (ANR-17-CE40-0022).Partially supported by Arnold O. Beckman Campus Research Board Award RB20003 of the University of Illinois at Urbana-Champaign, USA.
Publisher Copyright:
© 2021
PY - 2021/8
Y1 - 2021/8
N2 - A coloring of edges of a graph G is injective if for any two distinct edges e1 and e2, the colors of e1 and e2 are distinct if they are at distance 1 in G or in a common triangle. Naturally, the injective chromatic index of G, χinj′(G), is the minimum number of colors needed for an injective edge-coloring of G. We study how large can be the injective chromatic index of G in terms of maximum degree of G when we have restrictions on girth and/or chromatic number of G. We also compare our bounds with analogous bounds on the strong chromatic index.
AB - A coloring of edges of a graph G is injective if for any two distinct edges e1 and e2, the colors of e1 and e2 are distinct if they are at distance 1 in G or in a common triangle. Naturally, the injective chromatic index of G, χinj′(G), is the minimum number of colors needed for an injective edge-coloring of G. We study how large can be the injective chromatic index of G in terms of maximum degree of G when we have restrictions on girth and/or chromatic number of G. We also compare our bounds with analogous bounds on the strong chromatic index.
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U2 - 10.1016/j.ejc.2021.103355
DO - 10.1016/j.ejc.2021.103355
M3 - Article
AN - SCOPUS:85105339068
VL - 96
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
SN - 0195-6698
M1 - 103355
ER -