Non-bipartite k-common graphs
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866917756764422144 |
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| author | Kral, Daniel Noel, Jonathan A. Norin, Sergey Volec, Jan Wei, Fan |
| author_facet | Kral, Daniel Noel, Jonathan A. Norin, Sergey Volec, Jan Wei, Fan |
| contents | A graph H is k-common if the number of monochromatic copies of H in a k-edge-coloring of K_n is asymptotically minimized by a random coloring. For every k, we construct a connected non-bipartite k-common graph. This resolves a problem raised by Jagger, Stovicek and Thomason [Combinatorica 16 (1996), 123-141]. We also show that a graph H is k-common for every k if and only if H is Sidorenko and that H is locally k-common for every k if and only if H is locally Sidorenko. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_09422 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Non-bipartite k-common graphs Kral, Daniel Noel, Jonathan A. Norin, Sergey Volec, Jan Wei, Fan Combinatorics A graph H is k-common if the number of monochromatic copies of H in a k-edge-coloring of K_n is asymptotically minimized by a random coloring. For every k, we construct a connected non-bipartite k-common graph. This resolves a problem raised by Jagger, Stovicek and Thomason [Combinatorica 16 (1996), 123-141]. We also show that a graph H is k-common for every k if and only if H is Sidorenko and that H is locally k-common for every k if and only if H is locally Sidorenko. |
| title | Non-bipartite k-common graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2006.09422 |