The degree Ramsey number of a graph $G$, denoted $R_\Delta(G;s)$, is $\min\{\Delta(H)\colon\, H\stackrel{s}{\to} G\}$, where $H\stackrel{s}{\to} G$ means that every $s$-edge-coloring of $H$ contains a monochromatic copy of $G$. The closed $k$-blowup of a graph is obtained by replacing every vertex with a clique of size $k$ and every edge with a complete bipartite graph where both partite sets have size $k$. We prove that there is a function $f$ such that $R_\Delta(G;s) \le f(\Delta(G), s)$ when $G$ is a closed blowup of a tree.
@article{10_37236_2526,
author = {Paul Horn and Kevin G. Milans and Vojt\v{e}ch R\"odl},
title = {Degree {Ramsey} numbers of closed blowups of trees},
journal = {The electronic journal of combinatorics},
year = {2014},
volume = {21},
number = {2},
doi = {10.37236/2526},
zbl = {1300.05172},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2526/}
}
TY - JOUR
AU - Paul Horn
AU - Kevin G. Milans
AU - Vojtěch Rödl
TI - Degree Ramsey numbers of closed blowups of trees
JO - The electronic journal of combinatorics
PY - 2014
VL - 21
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/2526/
DO - 10.37236/2526
ID - 10_37236_2526
ER -
%0 Journal Article
%A Paul Horn
%A Kevin G. Milans
%A Vojtěch Rödl
%T Degree Ramsey numbers of closed blowups of trees
%J The electronic journal of combinatorics
%D 2014
%V 21
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/2526/
%R 10.37236/2526
%F 10_37236_2526
Paul Horn; Kevin G. Milans; Vojtěch Rödl. Degree Ramsey numbers of closed blowups of trees. The electronic journal of combinatorics, Tome 21 (2014) no. 2. doi: 10.37236/2526
