An open conjecture of Erdős states that for every positive integer $k$ there is a (least) positive integer $f(k)$ so that whenever a tournament has its edges colored with $k$ colors, there exists a set $S$ of at most $f(k)$ vertices so that every vertex has a monochromatic path to some point in $S$. We consider a related question and show that for every (finite or infinite) cardinal $\kappa>0$ there is a cardinal $ \lambda_\kappa $ such that in every $\kappa$-edge-coloured tournament there exist disjoint vertex sets $K,S$ with total size at most $ \lambda_\kappa$ so that every vertex $ v $ has a monochromatic path of length at most two from $K$ to $v$ or from $v$ to $S$.
@article{10_37236_6315,
author = {Krist\'of B\'erczi and Attila Jo\'o},
title = {King-serf duo by monochromatic paths in \(k\)-edge-coloured tournaments},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {1},
doi = {10.37236/6315},
zbl = {1358.05093},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6315/}
}
TY - JOUR
AU - Kristóf Bérczi
AU - Attila Joó
TI - King-serf duo by monochromatic paths in \(k\)-edge-coloured tournaments
JO - The electronic journal of combinatorics
PY - 2017
VL - 24
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/6315/
DO - 10.37236/6315
ID - 10_37236_6315
ER -
%0 Journal Article
%A Kristóf Bérczi
%A Attila Joó
%T King-serf duo by monochromatic paths in \(k\)-edge-coloured tournaments
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/6315/
%R 10.37236/6315
%F 10_37236_6315
Kristóf Bérczi; Attila Joó. King-serf duo by monochromatic paths in \(k\)-edge-coloured tournaments. The electronic journal of combinatorics, Tome 24 (2017) no. 1. doi: 10.37236/6315
