Disjoint connected dominating sets in pseudorandom graphs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912079793881088 |
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| author | Draganić, Nemanja Krivelevich, Michael |
| author_facet | Draganić, Nemanja Krivelevich, Michael |
| contents | A connected dominating set (CDS) in a graph is a dominating set of vertices that induces a connected subgraph. Having many disjoint CDSs in a graph can be considered as a measure of its connectivity, and has various graph-theoretic and algorithmic implications. We show that $d$-regular (weakly) pseudoreandom graphs contain $(1+o(1))d/\ln d$ disjoint CDSs, which is asymptotically best possible. In particular, this implies that random $d$-regular graphs typically contain $(1+o(1))d/\ln d$ disjoint CDSs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16072 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Disjoint connected dominating sets in pseudorandom graphs Draganić, Nemanja Krivelevich, Michael Combinatorics A connected dominating set (CDS) in a graph is a dominating set of vertices that induces a connected subgraph. Having many disjoint CDSs in a graph can be considered as a measure of its connectivity, and has various graph-theoretic and algorithmic implications. We show that $d$-regular (weakly) pseudoreandom graphs contain $(1+o(1))d/\ln d$ disjoint CDSs, which is asymptotically best possible. In particular, this implies that random $d$-regular graphs typically contain $(1+o(1))d/\ln d$ disjoint CDSs. |
| title | Disjoint connected dominating sets in pseudorandom graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2410.16072 |