无限snark族的全着色与公平全着色

RAIRO Oper. Res. Pub Date : 2023-09-05 DOI:10.1051/ro/2023129

M. Palma, Isabel Gonçalves, D. Sasaki, Simone Dantas

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引用次数: 0

摘要

我们证明了SemiBlowup, Blowup和第一Loupekine snark族的所有成员都有公平的总色数等于4。这些结果为Cavicchioli等人(2003)提出的问题提供了否定答案的证据:关于周长至少为5的2型蛇的最小阶;以及Dantas等人(2016)关于周长至少为5且总色数为5的1型三次图的存在性。此外，我们还展示了由Kochol叠加得到的一类新的无限族。

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On total coloring and equitable total coloring of infinite snark families

We show that all members of the SemiBlowup, Blowup and the first Loupekine snark families have equitable total chromatic number equal to 4. These results provide evidence of negative answers for the questions proposed: by Cavicchioli et al. (2003) about the smallest order of a Type 2 snark of girth at least 5; and by Dantas et al. (2016) about the existence of Type 1 cubic graph with girth at least 5 and equitable total chromatic number 5. Moreover, we show new infinite families of snarks obtained by the Kochol superpositions that are Type 1.

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RAIRO Oper. Res.

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