Tiling edge-coloured graphs with few monochromatic bounded-degree graphs

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Jan Corsten Walner Mendonça

Abstract

We prove that for all integers $\Delta,r \geq 2$, there is a constant $C = C(\Delta,r) >0$ such that the following is true for every sequence $\mathcal F = \{F_1, F_2, \ldots\}$ of graphs with $v(F_n) = n$ and $\Delta (F_n) \leq \Delta$ for every $n \in \mathbb N$. In every $r$-edge-coloured $K_n$, there is a collection of at most $C$ monochromatic copies from $\mathcal F$ whose vertex-sets partition $V(K_n)$. This makes progress on a conjecture of Grinshpun and S\'ark\"ozy.

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How to Cite
Corsten, J., & Mendonça, W. (2019). Tiling edge-coloured graphs with few monochromatic bounded-degree graphs. Acta Mathematica Universitatis Comenianae, 88(3), 561-566. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1212/694
Section
EUROCOMB 2019