On injective chromatic index of sparse graphs with maximum degree 5

Jian Lu (), Zhen-Mu Hong and Zheng-Jiang Xia
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Jian Lu: Anhui University of Finance & Economics
Zhen-Mu Hong: Anhui University of Finance & Economics
Zheng-Jiang Xia: Anhui University of Finance & Economics

Journal of Combinatorial Optimization, 2024, vol. 48, issue 5, No 5, 11 pages

Abstract: Abstract A k-edge coloring $$\varphi $$ φ of a graph G is injective if $$\varphi (e_1)\ne \varphi (e_3)$$ φ ( e 1 ) ≠ φ ( e 3 ) for any three consecutive edges $$e_1, e_2$$ e 1 , e 2 and $$e_3$$ e 3 of a path or a triangle. The injective chromatic index $$\chi _i'(G)$$ χ i ′ ( G ) of G is the smallest k such that G admits an injective k-edge coloring. By discharging method, we demonstrate that any graph with maximum degree $$\Delta \le 5$$ Δ ≤ 5 has $$\chi _i'(G)\le 12$$ χ i ′ ( G ) ≤ 12 (resp. 13) if its maximum average degree is less than $$\frac{20}{7}$$ 20 7 (resp. 3), which improves the results of Zhu (2023).

Keywords: Injective edge coloring; Injective chromatic index; Maximum average degree; 05C15 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10878-024-01234-7

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