On powers of circular arc graphs
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866913158159925248 |
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| author | Das, Ashok Kumar Paul, Indrajit |
| author_facet | Das, Ashok Kumar Paul, Indrajit |
| contents | A class of graphs $\mathcal{C}$ is closed under powers if for every graph $G\in\mathcal{C}$ and every $k\in\mathbb{N}$, $G^k\in\mathcal{C}$. Also $\mathcal{C}$ is strongly closed under powers if for every $k\in\mathbb{N}$, if $G^k\in\mathcal{C}$, then $G^{k+1}\in\mathcal{C}$. It is known that circular arc graphs and proper circular arc graphs are closed under powers. But it is open whether these classes of graphs are also strongly closed under powers. In this paper we have settled these problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_08782 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On powers of circular arc graphs Das, Ashok Kumar Paul, Indrajit Discrete Mathematics Combinatorics A class of graphs $\mathcal{C}$ is closed under powers if for every graph $G\in\mathcal{C}$ and every $k\in\mathbb{N}$, $G^k\in\mathcal{C}$. Also $\mathcal{C}$ is strongly closed under powers if for every $k\in\mathbb{N}$, if $G^k\in\mathcal{C}$, then $G^{k+1}\in\mathcal{C}$. It is known that circular arc graphs and proper circular arc graphs are closed under powers. But it is open whether these classes of graphs are also strongly closed under powers. In this paper we have settled these problems. |
| title | On powers of circular arc graphs |
| topic | Discrete Mathematics Combinatorics |
| url | https://arxiv.org/abs/2210.08782 |