Tiling with monochromatic bipartite graphs of bounded maximum degree
We prove that for any r∈N, there exists a constant Cr such that the following is true. Let F={F1,F2,…} be an infinite sequence of bipartite graphs such that |V(Fi)|=i and Δ(Fi)≤Δ hold for all i. Then in any r-edge coloured complete graph Kn, there is a collection of at most exp(CrΔ) monochromatic su...
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| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) Kapitel/Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
20 Sep 2021
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| In: |
Arxiv
Year: 2021, Pages: 1-18 |
| DOI: | 10.48550/arXiv.2109.09642 |
| Online-Zugang: | Verlag, kostenfrei, Volltext: https://doi.org/10.48550/arXiv.2109.09642 Verlag, kostenfrei, Volltext: http://arxiv.org/abs/2109.09642 
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| Verfasserangaben: | António Girão and Oliver Janzer |
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| 520 | |a We prove that for any r∈N, there exists a constant Cr such that the following is true. Let F={F1,F2,…} be an infinite sequence of bipartite graphs such that |V(Fi)|=i and Δ(Fi)≤Δ hold for all i. Then in any r-edge coloured complete graph Kn, there is a collection of at most exp(CrΔ) monochromatic subgraphs, each of which is isomorphic to an element of F, whose vertex sets partition V(Kn). This proves a conjecture of Corsten and Mendonça in a strong form and generalizes results on the multicolour Ramsey numbers of bounded-degree bipartite graphs. | ||
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