Neighborhood Balanced 3-Coloring
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910638679261184 |
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| author | Minyard, Mitchell Sepanski, Mark R. |
| author_facet | Minyard, Mitchell Sepanski, Mark R. |
| contents | A graph is said to be neighborhood 3-balanced if there exists a vertex labeling with three colors so that each vertex has an equal number of neighbors of each color. We give order constraints on 3-balanced graphs, determine which generalized Petersen and Pappus graphs are 3-balanced, discuss when being 3-balanced is preserved under various graph constructions, give two general characterizations of cubic 3-balanced graphs, and classify cubic 3-balanced graphs of small order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05422 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Neighborhood Balanced 3-Coloring Minyard, Mitchell Sepanski, Mark R. Combinatorics Primary: 05C15, Secondary: 05C69, 05C70, 05C75 A graph is said to be neighborhood 3-balanced if there exists a vertex labeling with three colors so that each vertex has an equal number of neighbors of each color. We give order constraints on 3-balanced graphs, determine which generalized Petersen and Pappus graphs are 3-balanced, discuss when being 3-balanced is preserved under various graph constructions, give two general characterizations of cubic 3-balanced graphs, and classify cubic 3-balanced graphs of small order. |
| title | Neighborhood Balanced 3-Coloring |
| topic | Combinatorics Primary: 05C15, Secondary: 05C69, 05C70, 05C75 |
| url | https://arxiv.org/abs/2410.05422 |