| Issue |
RAIRO-Oper. Res.
Volume 58, Number 3, May-June 2024
|
|
|---|---|---|
| Page(s) | 2367 - 2378 | |
| DOI | https://doi.org/10.1051/ro/2024098 | |
| Published online | 18 June 2024 | |
Complexity results on k-independence in some graph products*
Instituto of Informática, Universidade Federal of Goiás, Goiânia, Brazil
* Corresponding author: marcia@inf.ufg.br
Received:
8
February
2023
Accepted:
2
May
2024
For a positive integer k, a subset S of vertices of a graph G 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 the problem of determining k-independence remains NP-complete even for Cartesian products and complementary prisms. Furthermore, we present results on k-independence in the Cartesian product of two paths, known as grid graphs.
Mathematics Subject Classification: 05C69 / 05C76
Key words: Independence number / k-independent set / Cartesian product / complementary prism
© The authors. Published by EDP Sciences, ROADEF, SMAI 2024
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