1Fachbereich Mathematik, Universität Hamburg, Hamburg, Germany 2Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, Brazil 3IMPA, Rio de Janeiro, Brazil 4Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, Santo André, Brazil 5Institut für Mathematik, Technische Universität Ilmenau, Ilmenau, Germany
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 451-456
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Sören Berger; Yoshiharu Kohayakawa; Giulia Satiko Maesaka; Taísa Martins; Walner Mendonça; Guilherme Oliveira Mota; Olaf Parczyk; Sören Berger; Yoshiharu Kohayakawa; Giulia Satiko Maesaka; Taísa Martins; Walner Mendonça; Guilherme Oliveira Mota; Olaf Parczyk. The size-Ramsey number of powers of bounded degree trees. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 451-456. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a14/
@article{AMUC_2019_88_3_a14,
author = {S\"oren Berger and Yoshiharu Kohayakawa and Giulia Satiko Maesaka and Ta{\'\i}sa Martins and Walner Mendon\c{c}a and Guilherme Oliveira Mota and Olaf Parczyk and S\"oren Berger and Yoshiharu Kohayakawa and Giulia Satiko Maesaka and Ta{\'\i}sa Martins and Walner Mendon\c{c}a and Guilherme Oliveira Mota and Olaf Parczyk},
title = { The {size-Ramsey} number of powers of bounded degree trees},
journal = {Acta mathematica Universitatis Comenianae},
pages = {451--456},
year = {2019},
volume = {88},
number = {3},
url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a14/}
}
TY - JOUR
AU - Sören Berger
AU - Yoshiharu Kohayakawa
AU - Giulia Satiko Maesaka
AU - Taísa Martins
AU - Walner Mendonça
AU - Guilherme Oliveira Mota
AU - Olaf Parczyk
AU - Sören Berger
AU - Yoshiharu Kohayakawa
AU - Giulia Satiko Maesaka
AU - Taísa Martins
AU - Walner Mendonça
AU - Guilherme Oliveira Mota
AU - Olaf Parczyk
TI - The size-Ramsey number of powers of bounded degree trees
JO - Acta mathematica Universitatis Comenianae
PY - 2019
SP - 451
EP - 456
VL - 88
IS - 3
UR - http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a14/
ID - AMUC_2019_88_3_a14
ER -
%0 Journal Article
%A Sören Berger
%A Yoshiharu Kohayakawa
%A Giulia Satiko Maesaka
%A Taísa Martins
%A Walner Mendonça
%A Guilherme Oliveira Mota
%A Olaf Parczyk
%A Sören Berger
%A Yoshiharu Kohayakawa
%A Giulia Satiko Maesaka
%A Taísa Martins
%A Walner Mendonça
%A Guilherme Oliveira Mota
%A Olaf Parczyk
%T The size-Ramsey number of powers of bounded degree trees
%J Acta mathematica Universitatis Comenianae
%D 2019
%P 451-456
%V 88
%N 3
%U http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a14/
%F AMUC_2019_88_3_a14
Given an integer~$s \ge 1$, the \textit{$s$-colour size-Ramsey number} of a graph~$H$ is the smallest integer~$m$ such that there exists a graph~$G$ with~$m$ edges with the property that, in any colouring of~$E(G)$ with~$s$ colours, there is a monochromatic copy of~$H$. We prove that, for any positive integers~$k$ and~$s$, the $s$-colour size Ramsey number of the $k$th power of any $n$-vertex bounded degree tree is linear in~$n$.
