Injective coloring of planar graphs with girth 5

A coloring of a graph G is injective if its restriction to the neighbour of any vertex is injective. The injective chromatic number χ i ( G ) of a graph G is the least k such that there is an injective k -coloring. In this paper, we prove that for each planar graph with g ≥ 5 and Δ ( G ) ≥ 20, χ i (...

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Bibliographic Details
Published inFrontiers of mathematics in China Vol. 17; no. 3; pp. 473 - 484
Main Authors Bu, Yuehua, Ye, Piaopiao
Format Journal Article
LanguageEnglish
Published Beijing Higher Education Press 2022
Springer Nature B.V
Subjects
Coloring
Mathematics
Mathematics and Statistics
Research Article
05C10
girth
injective coloring
face
Planar graph
05C15
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Summary:A coloring of a graph G is injective if its restriction to the neighbour of any vertex is injective. The injective chromatic number χ i ( G ) of a graph G is the least k such that there is an injective k -coloring. In this paper, we prove that for each planar graph with g ≥ 5 and Δ ( G ) ≥ 20, χ i ( G ) ≤ Δ( G )+ 3.
ISSN:1673-3452
1673-3576
DOI:10.1007/s11464-022-1018-x