Maximum spread of $K_r$-minor free graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916470394454016 |
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| author | Wang, Wenyan Liu, Lele Wang, Yi |
| author_facet | Wang, Wenyan Liu, Lele Wang, Yi |
| contents | The spread of a graph is the difference between the largest and smallest eigenvalue of its adjacency matrix. In this paper, we investigate spread problems for graphs with excluded clique-minors. We show that for sufficiently large $n$, the $n$-vertex $K_r$-minor free graph with maximum spread is the join of a clique and an independent set, with $r-2$ and $n-r+2$ vertices, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04014 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximum spread of $K_r$-minor free graphs Wang, Wenyan Liu, Lele Wang, Yi Combinatorics The spread of a graph is the difference between the largest and smallest eigenvalue of its adjacency matrix. In this paper, we investigate spread problems for graphs with excluded clique-minors. We show that for sufficiently large $n$, the $n$-vertex $K_r$-minor free graph with maximum spread is the join of a clique and an independent set, with $r-2$ and $n-r+2$ vertices, respectively. |
| title | Maximum spread of $K_r$-minor free graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2411.04014 |