amphotericin

glassy

planar graph

coloring

chromatic number

maximum degree

chromatic number_99701

subgraph

monochromatic

distinguishing

European Journal of Combinatorics

A coloring of edges of a graph G is injective if for any two distinct edges e 1 and e 2 , the colors of e 1 and e 2 are distinct if they are at distance 1 in G or in a common triangle. Naturally, the injective chromatic index of G , χ inj ′ ( 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.

Injective edge-coloring of graphs with given maximum degree