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- Title
A NOTE ABOUT MONOCHROMATIC COMPONENTS IN GRAPHS OF LARGE MINIMUM DEGREE.
- Authors
DEBIASIO, LOUIS; KRUEGER, ROBERT A.
- Abstract
For all positive integers r ≥ 3 and n such that r² - r divides n and an affine plane of order r exists, we construct an r-edge colored graph on n vertices with minimum degree (...)n-2 such that the largest monochromatic component has order less than ... . This generalizes an example of Guggiari and Scott and, independently, Rahimi for r = 3 and thus disproves a conjecture of Gyárfás and Sárközy for all integers r ≥ 3 such that an affine plane of order r exists.
- Subjects
RAMSEY numbers; RAMSEY theory; INTEGERS
- Publication
Discussiones Mathematicae: Graph Theory, 2023, Vol 43, Issue 3, p607
- ISSN
1234-3099
- Publication type
Article
- DOI
10.7151/dmgt.2390