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

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 c...

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Bibliographic Details
Published inJournal of combinatorial optimization Vol. 44; no. 2; pp. 1356 - 1375
Main Authors La, Hoang, Montassier, Mickael
Format Journal Article
LanguageEnglish
Published New York Springer US 01.09.2022
Springer Nature B.V
Springer Verlag
Subjects
Apexes
Color
Coloring
Combinatorics
Convex and Discrete Geometry
Graph theory
Graphs
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Theory of Computation
2-distance coloring
Planar graphs
Discharging method
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Summary: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 ( Δ + 2 )-coloring for planar graphs with girth at least 10 and maximum degree Δ ≥ 4 .
ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-022-00883-w