Injective edge coloring of graphs with maximum degree 5
2023; Elsevier BV; Volume: 334; Linguagem: Inglês
10.1016/j.dam.2023.03.022
ISSN1872-6771
Autores Tópico(s)Limits and Structures in Graph Theory
ResumoA k-injective-edge coloring of a graph G is an edge coloring c:E(G)→{1,2,…,k} such that c(e1)≠c(e3) for any three consecutive edges e1,e2,e3 of a path or a 3-cycle. The minimum integer k such that G has a k-injective-edge coloring is called the injective chromatic index of G, denoted by χi′(G). In this paper, we prove that for graphs G with Δ(G)≤5, it is 13-injective-edge colorable if mad(G)<145 and it is 14-injective-edge colorable if mad(G)<3, where mad(G)=max{2|E(H)||V(H)|,H⊆G} denotes the maximum average degree of G.
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