Letzter, Shoham;
(2022)
An improvement on Łuczak's connected matchings method.
Bulletin of the London Mathematical Society
, 54
(2)
pp. 609-623.
10.1112/blms.12587.
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Abstract
A connected matching in a graph G is a matching contained in a connected component of G. A well-known method due to Łuczak reduces problems about monochromatic paths and cycles in complete graphs to problems about monochromatic connected matchings in almost complete graphs. We show that these can be further reduced to problems about monochromatic connected matchings in complete graphs. We illustrate the potential of this new reduction by showing how it can be used to determine the 3-colour Ramsey number of long paths, using a simpler argument than the original one by Gyárfás, Ruszinkó, Sárközy, and Szemerédi (2007).
| Type: | Article |
|---|---|
| Title: | An improvement on Łuczak's connected matchings method |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1112/blms.12587 |
| Publisher version: | https://doi.org/10.1112/blms.12587 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10148495 |
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