Sharp upper bound of injective coloring of planar graphs with girth at least 5

Qiming Fang () and Li Zhang ()
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Qiming Fang: Tongji University
Li Zhang: Tongji University

Journal of Combinatorial Optimization, 2022, vol. 44, issue 2, No 14, 1198 pages

Abstract: Abstract An injective k-coloring of a graph G is a k-coloring c (not necessarily proper) such that $$c(u)\ne c(v)$$ c ( u ) ≠ c ( v ) whenever u, v has a common neighbor in G. The injective chromatic number of G, denoted by $$\chi _i(G)$$ χ i ( G ) , is the least integer k such that G has an injective k-coloring. We prove that the injective chromatic number of planar graphs with $$g \ge 5$$ g ≥ 5 and $$\Delta \ge 2339$$ Δ ≥ 2339 is at most $$\Delta + 1$$ Δ + 1 , and this bound is sharp.

Keywords: Injective Coloring; Planar graphs; Discharging; 05C15 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10878-022-00880-z

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