The size-Ramsey number $\hat{R}(F,r)$ of a graph $F$ is the smallest integer $m$ such that there exists a graph $G$ on $m$ edges with the property that any colouring of the edges of $G$ with $r$ colours yields a monochromatic copy of $F$. In this short note, we give an alternative proof of the recent result of Krivelevich that $\hat{R}(P_n,r) = O((\log r)r^2 n)$. This upper bound is nearly optimal, since it is also known that $\hat{R}(P_n,r) = \Omega(r^2 n)$.
@article{10_37236_7954,
author = {Andrzej Dudek and Pawe{\l} Pra{\l}at},
title = {Note on the multicolour {size-Ramsey} number for paths},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {3},
doi = {10.37236/7954},
zbl = {1395.05179},
url = {http://geodesic.mathdoc.fr/articles/10.37236/7954/}
}
TY - JOUR
AU - Andrzej Dudek
AU - Paweł Prałat
TI - Note on the multicolour size-Ramsey number for paths
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/7954/
DO - 10.37236/7954
ID - 10_37236_7954
ER -
%0 Journal Article
%A Andrzej Dudek
%A Paweł Prałat
%T Note on the multicolour size-Ramsey number for paths
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/7954/
%R 10.37236/7954
%F 10_37236_7954
Andrzej Dudek; Paweł Prałat. Note on the multicolour size-Ramsey number for paths. The electronic journal of combinatorics, Tome 25 (2018) no. 3. doi: 10.37236/7954
