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Sub-Ramsey Numbers for Matchings.
- Source :
- Graphs & Combinatorics; Nov2020, Vol. 36 Issue 6, p1675-1685, 11p
- Publication Year :
- 2020
-
Abstract
- Given a graph G and a positive integer k, the sub-Ramsey number sr(G, k) is defined to be the minimum number m such that every K m whose edges are colored using every color at most k times contains a subgraph isomorphic to G all of whose edges have distinct colors. In this paper, we will concentrate on s r (n K 2 , k) with n K 2 denoting a matching of size n. We first give upper and lower bounds for s r (n K 2 , k) and exact values of s r (n K 2 , k) for some n and k. Afterwards, we show that s r (n K 2 , k) = 2 n when n is sufficiently large and k < n 8 by applying the Local Lemma. [ABSTRACT FROM AUTHOR]
- Subjects :
- RAMSEY numbers
INTEGERS
COLORS
CHROMATIC polynomial
EDGES (Geometry)
Subjects
Details
- Language :
- English
- ISSN :
- 09110119
- Volume :
- 36
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- Graphs & Combinatorics
- Publication Type :
- Academic Journal
- Accession number :
- 146479629
- Full Text :
- https://doi.org/10.1007/s00373-020-02216-2