On the complexity of Dominating Set for graphs with fixed diameter
| Autor: | Bouquet, Valentin, Delbot, François, Picouleau, Christophe, Rovedakis, Stéphane |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | A set $S\subseteq V$ of a graph $G=(V,E)$ is a dominating set if each vertex has a neighbor in $S$ or belongs to $S$. Dominating Set is the problem of deciding, given a graph $G$ and an integer $k\geq 1$, if $G$ has a dominating set of size at most $k$. It is well known that this problem is $\mathsf{NP}$-complete even for claw-free graphs. We give a complexity dichotomy for Dominating Set for the class of claw-free graphs with diameter $d$. We show that the problem is $\mathsf{NP}$-complete for every fixed $d\ge 3$ and polynomial time solvable for $d\le 2$. To prove the case $d=2$, we show that Minimum Maximal Matching can be solved in polynomial time for $2K_2$-free graphs. Comment: 15 pages, 5 figures |
| Databáze: | arXiv |
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