Backbone coloring for graphs with degree 4
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909317370740736 |
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| author | Michalik, Krzysztof Turowski, Krzysztof |
| author_facet | Michalik, Krzysztof Turowski, Krzysztof |
| contents | The $λ$-backbone coloring of the graph $G$ with backbone $H$ is a graph-coloring problem in which we are given a graph $G$ and a subgraph $H$, and we want to assign colors to vertices in such a way that the endpoints of every edge from $G$ have different colors, and the endpoints of every edge from $H$ are assigned colors which differ by at least $λ$.
In this paper we pursue research on backbone coloring of bounded-degree graphs with well-known classes of backbones. Our result is an almost complete classification of problems in the form $BBC_λ(G, H) \le λ+ k$ for graphs with maximum degree $4$ and backbones from the following classes: paths, trees, matchings, and galaxies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10201 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Backbone coloring for graphs with degree 4 Michalik, Krzysztof Turowski, Krzysztof Combinatorics 05C15, 05C78, 68R05 G.2.2 The $λ$-backbone coloring of the graph $G$ with backbone $H$ is a graph-coloring problem in which we are given a graph $G$ and a subgraph $H$, and we want to assign colors to vertices in such a way that the endpoints of every edge from $G$ have different colors, and the endpoints of every edge from $H$ are assigned colors which differ by at least $λ$. In this paper we pursue research on backbone coloring of bounded-degree graphs with well-known classes of backbones. Our result is an almost complete classification of problems in the form $BBC_λ(G, H) \le λ+ k$ for graphs with maximum degree $4$ and backbones from the following classes: paths, trees, matchings, and galaxies. |
| title | Backbone coloring for graphs with degree 4 |
| topic | Combinatorics 05C15, 05C78, 68R05 G.2.2 |
| url | https://arxiv.org/abs/2409.10201 |