Coloring the square of maximal planar graphs with diameter two

Yiqiao Wang, Jingjing Huo, Jiangxu Kong and Qiuyue Tan

Applied Mathematics and Computation, 2023, vol. 459, issue C

Abstract: Let G be a maximal planar graph with diameter two and maximum degree Δ. Let χ(G2) denote the chromatic number of the square of G. In this paper, we prove that χ(G2)=Δ+1 if 2≤Δ≤3; χ(G2)≤6 if Δ=4; χ(G2)≤9 if Δ=5; χ(G2)≤Δ+5 if 6≤Δ≤7; and χ(G2)≤⌊3Δ/2⌋+1 if Δ≥8. All bounds are tight. This confirms the Wegner's conjecture for maximal planar graphs with diameter two.

Keywords: Wegner's conjecture; Chromatic number; Maximal planar graph; Diameter (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:459:y:2023:i:c:s0096300323004320

DOI: 10.1016/j.amc.2023.128263

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