1LSE, Houghton St, London, UK 2IMPA, Estrada Dona Castorina, Rio de Janeiro, Brazil
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 561-566
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Jan Corsten; Walner Mendonça; Jan Corsten; Walner Mendonça. Tiling edge-coloured graphs with few monochromatic bounded-degree graphs. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 561-566. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a32/
@article{AMUC_2019_88_3_a32,
author = {Jan Corsten and Walner Mendon\c{c}a and Jan Corsten and Walner Mendon\c{c}a},
title = { Tiling edge-coloured graphs with few monochromatic bounded-degree graphs},
journal = {Acta mathematica Universitatis Comenianae},
pages = {561--566},
year = {2019},
volume = {88},
number = {3},
url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a32/}
}
TY - JOUR
AU - Jan Corsten
AU - Walner Mendonça
AU - Jan Corsten
AU - Walner Mendonça
TI - Tiling edge-coloured graphs with few monochromatic bounded-degree graphs
JO - Acta mathematica Universitatis Comenianae
PY - 2019
SP - 561
EP - 566
VL - 88
IS - 3
UR - http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a32/
ID - AMUC_2019_88_3_a32
ER -
%0 Journal Article
%A Jan Corsten
%A Walner Mendonça
%A Jan Corsten
%A Walner Mendonça
%T Tiling edge-coloured graphs with few monochromatic bounded-degree graphs
%J Acta mathematica Universitatis Comenianae
%D 2019
%P 561-566
%V 88
%N 3
%U http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a32/
%F AMUC_2019_88_3_a32
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.
