Unified bounds for the independence number of graph powers
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913578025484288 |
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| author | Abiad, Aida Zhou, Jiang |
| author_facet | Abiad, Aida Zhou, Jiang |
| contents | For a graph $G$, its $k$-th power $G^k$ is constructed by placing an edge between two vertices if they are within distance $k$ of each other. The $k$-independence number $α_k(G)$ is defined as the independence number of $G^k$. By using general semidefinite programming and polynomial methods, we derive sharp bounds for the $k$-independence number of a graph, which extend and unify various existing results. Our work also allows us to easily derive some new bounds for $α_k(G)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09450 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unified bounds for the independence number of graph powers Abiad, Aida Zhou, Jiang Combinatorics For a graph $G$, its $k$-th power $G^k$ is constructed by placing an edge between two vertices if they are within distance $k$ of each other. The $k$-independence number $α_k(G)$ is defined as the independence number of $G^k$. By using general semidefinite programming and polynomial methods, we derive sharp bounds for the $k$-independence number of a graph, which extend and unify various existing results. Our work also allows us to easily derive some new bounds for $α_k(G)$. |
| title | Unified bounds for the independence number of graph powers |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2411.09450 |