Biclique immersions in graphs with independence number 2
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913467932344320 |
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| author | Botler, Fábio Jiménez, Andrea Lintzmayer, Carla N. Pastine, Adrián Quiroz, Daniel A. Sambinelli, Maycon |
| author_facet | Botler, Fábio Jiménez, Andrea Lintzmayer, Carla N. Pastine, Adrián Quiroz, Daniel A. Sambinelli, Maycon |
| contents | The analogue of Hadwiger's conjecture for the immersion relation states that every graph $G$ contains an immersion of $K_{χ(G)}$. For graphs with independence number 2, this is equivalent to stating that every such $n$-vertex graph contains an immersion of $K_{\lceil n/2 \rceil}$. We show that every $n$-vertex graph with independence number 2 contains every complete bipartite graph on $\lceil n/2 \rceil$ vertices as an immersion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_06483 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Biclique immersions in graphs with independence number 2 Botler, Fábio Jiménez, Andrea Lintzmayer, Carla N. Pastine, Adrián Quiroz, Daniel A. Sambinelli, Maycon Combinatorics Discrete Mathematics The analogue of Hadwiger's conjecture for the immersion relation states that every graph $G$ contains an immersion of $K_{χ(G)}$. For graphs with independence number 2, this is equivalent to stating that every such $n$-vertex graph contains an immersion of $K_{\lceil n/2 \rceil}$. We show that every $n$-vertex graph with independence number 2 contains every complete bipartite graph on $\lceil n/2 \rceil$ vertices as an immersion. |
| title | Biclique immersions in graphs with independence number 2 |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2303.06483 |