3-Coloring on Regular, Planar, and Ordered Hamiltonian Graphs
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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≥ 6 and p-ordered regular Hamiltonian graphs for every p≥ 3.
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