2-Distance list $$(\Delta +2)$$ ( Δ + 2 ) -coloring of planar graphs with girth at least 10

Hoang La () and Mickael Montassier ()
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Hoang La: LIRMM, Université de Montpellier, CNRS
Mickael Montassier: LIRMM, Université de Montpellier, CNRS

Journal of Combinatorial Optimization, 2022, vol. 44, issue 2, No 22, 1356-1375

Abstract: Abstract Given a graph G and a list assignment L(v) for each vertex of v of G, a proper L-list-coloring of G is a function that maps every vertex to a color in L(v) such that no pair of adjacent vertices have the same color. We say that a graph is k-list-colorable when every vertex v has a list of colors of size at least k. A 2-distance coloring is a coloring where vertices at distance at most 2 cannot share the same color. We prove the existence of a 2-distance list ( $$\Delta +2$$ Δ + 2 )-coloring for planar graphs with girth at least 10 and maximum degree $$\Delta \ge 4$$ Δ ≥ 4 .

Keywords: Planar graphs; 2-distance coloring; Discharging method (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10878-022-00883-w

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