Decompositions of edge-coloured infinite complete graphs into monochromatic paths II
Combinatorics
2016-03-17 v2 Logic
Abstract
P. Erd\H{o}s proved that every 2-edge coloured complete graph on the natural numbers can be vertex decomposed into two monochromatic paths of different colour. This result was extended by R. Rado to an arbitrary finite number of colours. We prove that the vertices of every finite-edge coloured infinite complete graph can be partitioned into disjoint monochromatic paths of different colours. This answers a question of R. Rado from 1978.
Keywords
Cite
@article{arxiv.1507.06187,
title = {Decompositions of edge-coloured infinite complete graphs into monochromatic paths II},
author = {Daniel T. Soukup},
journal= {arXiv preprint arXiv:1507.06187},
year = {2016}
}
Comments
32 pages, minor changes made to previous version, accepted at the Israel Journal of Mathematics