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Совершенные раскраски скрещенной призмы Full article

Journal Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304
Output data Year: 2025, Volume: 22, Number: 2, Pages: 1138-1153 Pages count : 16 DOI: 10.33048/semi.2025.22.070
Tags crossed prism graph, perfect coloring, disjunctive perfect coloring
Authors Лисицына М.А. 1 , Августинович С.В. 2
Affiliations
1 Mozhaisky Military Space Academy, Zhdanovskaya, 13, 197198, St Petersburg
2 Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk

Funding (1)

1 Sobolev Institute of Mathematics FWNF-2022-0017

Abstract: A coloring of vertices of a given graph is called perfect if the color structure of each sphere of radius 1 in the graph depends only on the color of the sphere center. The crossed prism graph is a graph obtained by taking two disjoint infinite cycles (the vertices of the upper cycle are even integers, and the vertices of the lower cycle are odd ones) and adding edges (i,i+3) for i=4p and (i,i−1) for i=4p+2 (p∈Z ). A complete description of perfect colorings with an arbitrary number of colors is obtained for crossed prism graph. It is proved that all its perfect colorings are exhausted by disjunctive ones, except for six sporadic cases.
Cite: Лисицына М.А. , Августинович С.В.
Совершенные раскраски скрещенной призмы
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2025. Т.22. №2. С.1138-1153. DOI: 10.33048/semi.2025.22.070
Dates:
Submitted: Feb 14, 2025
Published print: Oct 11, 2025
Published online: Oct 11, 2025
Identifiers: No identifiers
Citing: Пока нет цитирований
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