2-distance, injective, and exact square list-coloring of planar graphs with maximum degree 4 - LIRMM - Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier Access content directly
Journal Articles Discrete Mathematics Year : 2023

2-distance, injective, and exact square list-coloring of planar graphs with maximum degree 4

Xuan Hoang La
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Abstract

In the past various distance based colorings on planar graphs were introduced. We turn our focus to three of them, namely 2-distance coloring, injective coloring, and exact square coloring. A 2-distance coloring is a proper coloring of the vertices in which no two vertices at distance 2 receive the same color, an injective coloring is a coloring of the vertices in which no two vertices with a common neighbor receive the same color, and an exact square coloring is a coloring of the vertices in which no two vertices at distance exactly 2 receive the same color. We prove that planar graphs with maximum degree ∆ = 4 and girth at least 4 are 2-distance list (∆+7)-colorable and injectively list (∆ + 5)-colorable. Additionally, we prove that planar graphs with ∆ = 4 are injectively list (∆ + 7)-colorable and exact square list (∆ + 6)-colorable.

Dates and versions

lirmm-04042004 , version 1 (22-03-2023)

Identifiers

Cite

Xuan Hoang La, Kenny Štorgel. 2-distance, injective, and exact square list-coloring of planar graphs with maximum degree 4. Discrete Mathematics, 2023, 346 (8), pp.#113405. ⟨10.1016/j.disc.2023.113405⟩. ⟨lirmm-04042004⟩
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