Rainbow Cliques in Edge-Colored 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_ | 1866910522868236288 |
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| author | Czygrinow, Andrzej Molla, Theodore Nagle, Brendan |
| author_facet | Czygrinow, Andrzej Molla, Theodore Nagle, Brendan |
| contents | Let $G = (V,E)$ be an $n$-vertex graph and let $c: E \to \mathbb{N}$ be a coloring of its edges. Let $d^c(v)$ be the number of distinct colors on the edges at $v \in V$ and let $δ^c(G) = \min_{v \in V} \{ d^{c}(v) \}$. H. Li proved that $δ^c(G) > n/2$ guarantees a rainbow triangle in $G$. We give extensions of Li's result to cliques $K_r$ for $r \ge 4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08098 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rainbow Cliques in Edge-Colored Graphs Czygrinow, Andrzej Molla, Theodore Nagle, Brendan Combinatorics Let $G = (V,E)$ be an $n$-vertex graph and let $c: E \to \mathbb{N}$ be a coloring of its edges. Let $d^c(v)$ be the number of distinct colors on the edges at $v \in V$ and let $δ^c(G) = \min_{v \in V} \{ d^{c}(v) \}$. H. Li proved that $δ^c(G) > n/2$ guarantees a rainbow triangle in $G$. We give extensions of Li's result to cliques $K_r$ for $r \ge 4$. |
| title | Rainbow Cliques in Edge-Colored Graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2407.08098 |