On the $δ$-chromatic numbers of the Cartesian products of graphs
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910285240991744 |
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| author | Tangjai, Wipawee Pho-on, Witsarut Vichitkunakorn, Panupong |
| author_facet | Tangjai, Wipawee Pho-on, Witsarut Vichitkunakorn, Panupong |
| contents | In this work, we study the $δ$-chromatic number of a graph which is the chromatic number of the $δ$-complement of a graph. We give a structure of the $δ$-complements and sharp bounds on the $δ$-chromatic numbers of the Cartesian products of graphs. Furthermore, we compute the $δ$-chromatic numbers of various classes of Cartesian product graphs, including the Cartesian products between cycles, paths, and stars. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00666 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the $δ$-chromatic numbers of the Cartesian products of graphs Tangjai, Wipawee Pho-on, Witsarut Vichitkunakorn, Panupong Combinatorics 05C07, 05C15, 05C35, 05C38, 05C69 In this work, we study the $δ$-chromatic number of a graph which is the chromatic number of the $δ$-complement of a graph. We give a structure of the $δ$-complements and sharp bounds on the $δ$-chromatic numbers of the Cartesian products of graphs. Furthermore, we compute the $δ$-chromatic numbers of various classes of Cartesian product graphs, including the Cartesian products between cycles, paths, and stars. |
| title | On the $δ$-chromatic numbers of the Cartesian products of graphs |
| topic | Combinatorics 05C07, 05C15, 05C35, 05C38, 05C69 |
| url | https://arxiv.org/abs/2401.00666 |