On Strong Edge-Coloring of Claw-Free Subcubic Graphs

Lv, Jian-Bo; Li, Jianxi; Zhang, Xiaoxia

doi:10.1007/s00373-022-02462-6

Cited by 5 publications

(4 citation statements)

References 10 publications

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“…Remark 1. Recall that when ∆(G) = 3, the upper bound in Conjecture 1.1 is 10, the upper bound in Theorem 1.2 is 105 8 , and the upper bound proved by Lv, Li and Zhang [18] is 8, while our bound in Theorem 1.3 is 7.…”

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confidence: 75%

“…A graph with maximum degree less than or equal to 3 is called a subcubic graph. In 2022, Lv, Li and Zhang [18] proved that, for any claw-free subcubic graph G other than the triangular prism, χ s (G) ≤ 8. Please see Figure 1 for the triangular prism (also called the 3-prism).…”

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confidence: 99%

“…Remark 2. A graph G 0 on five vertices with strong chromatic index 7 was presented in [18] (see Figure 2). This shows the sharpness of the upper bound 7.…”

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confidence: 99%

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The tight bound for the strong chromatic indices of claw-free subcubic graphs

Lin¹,

Lin²

2022

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Let G be a graph and k a positive integer. A strong k-edge-coloring of G is a mapping φ : E(G) → {1, 2, . . . , k} such that for any two edges e and e that are either adjacent to each other or adjacent to a common edge, φ(e) = φ(e ). The strong chromatic index of G, denoted as χ s (G), is the minimum integer k such that G has a strong k-edge-coloring. Lv, Li and Zhang [Graphs and Combinatorics 38 (3) ( 2022) 63] proved that if G is a claw-free subcubic graph other than the triangular prism then χ s (G) ≤ 8. In addition, they asked if the upper bound 8 can be improved to 7. In this paper, we answer this question in the affirmative. Our proof implies a linear-time algorithm for finding strong 7-edge-colorings of such graphs. We also construct infinitely many claw-free subcubic graphs with their strong chromatic indices attaining the bound 7.

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confidence: 75%

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confidence: 99%

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The tight bound for the strong chromatic indices of claw-free subcubic graphs

Lin¹,

Lin²

2022

Preprint

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“…In 2022, Lv, Li and Zhang [14] proved that, for any claw-free subcubic graph G other than the triangular prism, χ s (G) ≤ 8. Please see Figure 2 for the triangular prism (also called the 3-prism).…”

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confidence: 99%