关于某些图积中 k-independence 的复杂性结果

RAIRO - Operations Research Pub Date : 2024-05-07 DOI:10.1051/ro/2024098

Márcia Cappelle, Erika Coelho, Otavio Mortosa, Julliano Nascimento

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引用次数: 0

摘要

对于正整数 k，如果 S 中的每个顶点在 S 中最多有 k - 1 个相邻顶点，则图 G=(V,E)的顶点子集 S 是 k-independent 的：笛卡尔图和互补棱镜图。我们证明，即使对于笛卡尔积和互补棱图，k-independence 仍然是 NP-complete。此外，我们还介绍了网格图中的 k-independence 结果，网格图是两条路径的笛卡尔积。

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Complexity results on k-independence in some graph products

For a positive integer k, a subset S of vertices of a graph G=(V,E) is k-independent if each vertex in S has at most k - 1 neighbors in S. We consider k-independent sets in two graph products: Cartesian and complementary prism. We show that k-independence remains NP-complete even for Cartesian products and complementary prisms. Furthermore, we present results on k-independence in grid graphs, which is a Cartesian product of two paths.

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RAIRO - Operations Research

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