Article Dans Une Revue Discrete Mathematics Letters Année : 2025

On the [r, s, t]-coloring of the square of cylindrical grids

Résumé

The [r,s,t]-coloring is a generalization of the classical vertex, edge, and total colorings, where two vertices, two edges, and a vertex and its incident edges have colors distant by at least r, s and t, respectively. The square of a graph G is a graph obtained from G by adding an edge between two vertices at a distance at most 2 in G. A cylindrical grid is equivalent to the Cartesian product of a path and a cycle. In this article, colorings for the square of cylindrical grids are discussed. It is shown that such graphs are class one graphs (according to Vizing’s theorem). For the [r,s,t]-coloring of these graphs, particular values of r, s and t are presented, for which the minimum number of colors needed in an [r,s,t]-coloring is determined.

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Dates et versions

hal-04892915 , version 1 (02-05-2025)

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Brice Effantin. On the [r, s, t]-coloring of the square of cylindrical grids. Discrete Mathematics Letters, 2025, 15, pp.15-22. ⟨10.47443/dml.2024.148⟩. ⟨hal-04892915⟩
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