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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2302.08708 |
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| _version_ | 1866929235403210752 |
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| author | Shaebani, Saeed |
| author_facet | Shaebani, Saeed |
| contents | \noindent In this paper, we show that for any positive integers $r$, $k$, $Θ$, and $Γ$ such that $k \geq 2$ and $r \geq k + Γ$, there exists a connected graph $G$ for which $$\begin{array}{llcr}
ω(G) = χ(G) = k, & χ\left( G , rK_2 \right) = Θ, & {\rm and} & |E(G)| - {\rm ex}\left( G , rK_2 \right) = Θ+ Γ. \end{array}$$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_08708 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Matching Kneser Graph Conjecture For High Chromatic Numbers Shaebani, Saeed Combinatorics \noindent In this paper, we show that for any positive integers $r$, $k$, $Θ$, and $Γ$ such that $k \geq 2$ and $r \geq k + Γ$, there exists a connected graph $G$ for which $$\begin{array}{llcr} ω(G) = χ(G) = k, & χ\left( G , rK_2 \right) = Θ, & {\rm and} & |E(G)| - {\rm ex}\left( G , rK_2 \right) = Θ+ Γ. \end{array}$$ |
| title | The Matching Kneser Graph Conjecture For High Chromatic Numbers |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2302.08708 |