On injective edge coloring of sparse graphs with maximum degree 5

Yanqing Wu ()
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Yanqing Wu: Shanxi Normal University

Journal of Combinatorial Optimization, 2025, vol. 50, issue 4, No 1, 21 pages

Abstract: Abstract A k-injective-edge coloring of a graph G is an edge coloring c: $$E(G)\rightarrow \{1,2,\cdots ,k\}$$ , such that if $$e_{1}$$ , $$e_{2}$$ and $$e_{3}$$ are three consecutive edges in G, then $$c(e_{1})\ne c(e_{3})$$ , where $$e_{1}$$ , $$e_{2}$$ and $$e_{3}$$ are consecutive if they form a path or a cycle of length 3. The minimum integer k such that G has a k-injective-edge coloring is called the injective chromatic index of G, denoted by $$\chi '_{i}(G)$$ . The maximum average degree of G, denoted by mad(G), is defined to be the maximum average over all subgraphs H of G. In this paper, I will consider the injective edge coloring of sparse graph G with maximum degree 5. I get that (1) if mad $$(G)

Keywords: Maximum degree; Maximum average degree; Injective edge coloring; Injective chromatic index; 05C15 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10878-025-01362-8

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