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Article Dans Une Revue Discrete Mathematics Année : 2024

About S-packing coloring of subcubic graphs

A propos de la coloration de S-packing des graphes sous-cubiques

Résumé

For a non-decreasing sequence of integers (a1, a2, . . . , ak ), an (a1, a2, . . . , ak )-packing coloring of a graph G is a partition of V (G) into k subsets V 1, V 2, . . . , V k such that the distance between any two distinct vertices x, y ∈ V i is at least a i + 1, 1 ≤ i ≤ k. This paper studies the packing coloring of subcubic graphs. Gastineau and Togni (2016) [7] asked whether every subcubic graph except the Petersen graph is (1, 1, 2, 3)-packing colorable. A subcubic graph G is said to be i-saturated, 0 ≤ i ≤ 2, if every vertex of degree three in G has at most i neighbors of degree three and it is said to be 3-saturated if it is not 2-saturated. Besides, a vertex of degree three in a 3-saturated subcubic graph is said to be heavy if all its neighbors are of degree three. We prove that every 1-saturated subcubic graph is (1, 1, 2)-packing colorable. Moreover, we prove that a 3-saturated subcubic graph is (1, 1, 2, 2)-packing colorable if any two of its heavy vertices are not adjacent.
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Dates et versions

hal-04469182 , version 1 (20-02-2024)

Identifiants

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Maidoun Mortada, Olivier Togni. About S-packing coloring of subcubic graphs. Discrete Mathematics, 2024, 347 (5), pp.113917. ⟨10.1016/j.disc.2024.113917⟩. ⟨hal-04469182⟩
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