3-Coloring on Regular, Planar, and Ordered Hamiltonian Graphs

Dario Cavallaro; Till Fluschnik

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arXiv · 2104.08470

3-Coloring on Regular, Planar, and Ordered Hamiltonian Graphs

Dario Cavallaro·Till Fluschnik

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Abstract

We prove that 3-Coloring remains NP-hard on 4- and 5-regular planar Hamiltonian graphs, strengthening the results of Dailey [Disc. Math.'80] and Fleischner and Sabidussi [J. Graph. Theor.'02]. Moreover, we prove that 3-Coloring remains NP-hard on $p$-regular Hamiltonian graphs for every $p\geq 6$ and $p$-ordered regular Hamiltonian graphs for every $p\geq 3$.

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Dario Cavallaro, Till Fluschnik. 2021-04-17. 3-Coloring on Regular, Planar, and Ordered Hamiltonian Graphs. https://arxiv.org/abs/2104.08470

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