Ramsey and Gallai-Ramsey Number for Wheels
Given a graph G and a positive integer k , define the Gallai-Ramsey number to be the minimum number of vertices n such that any k -edge coloring of K n contains either a rainbow (all different colored) triangle or a monochromatic copy of G . Much like graph Ramsey numbers, Gallai-Ramsey numbers have...
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Veröffentlicht in: | Graphs and combinatorics 2022-04, Vol.38 (2), Article 42 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | Given a graph
G
and a positive integer
k
, define the
Gallai-Ramsey number
to be the minimum number of vertices
n
such that any
k
-edge coloring of
K
n
contains either a rainbow (all different colored) triangle or a monochromatic copy of
G
. Much like graph Ramsey numbers, Gallai-Ramsey numbers have gained a reputation as being very difficult to compute in general. As yet, still only precious few sharp results are known. In this paper, we obtain bounds on the Gallai-Ramsey number for wheels and the exact value for the wheel on 5 vertices. |
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ISSN: | 0911-0119 1435-5914 |
DOI: | 10.1007/s00373-021-02406-6 |