On 3-coloured tournaments
Agelos Georgakopoulos, Philipp Spr\"ussel
TL;DR
This paper proves that in any 3-coloured tournament without a vertex incident with all colours, there exists either a rainbow triangle or a vertex that monochromatically dominates all others.
Contribution
It provides a new proof of a combinatorial property of 3-coloured tournaments, highlighting the existence of specific substructures under certain conditions.
Findings
Existence of a cyclic rainbow triangle or a dominating vertex in specified tournaments
The proof applies to tournaments with no vertex incident with all three colours
Clarifies structure of 3-coloured tournaments with restricted incident colours
Abstract
We (re-)prove that in every 3-edge-coloured tournament in which no vertex is incident with all colours there is either a cyclic rainbow triangle or a vertex dominating every other vertex monochromatically.
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Taxonomy
TopicsBusiness Strategy and Innovation · graph theory and CDMA systems