Webb1 jan. 1977 · A probability theorem, due to Lovasz, is used to derive lower bounds for various Ramsey functions. A short proof of the known result R (3, t) ⩾ ct 2 ln t) 2 is given. … Webb22 sep. 2024 · Abstract: We give an exponential improvement to the lower bound on diagonal Ramsey numbers for any fixed number of colors greater than two. Comments: 4 pages: Subjects: Combinatorics (math.CO) Cite as: arXiv:2009.10458 [math.CO] (or arXiv:2009.10458v3 [math.CO] for this version)
[2009.10458] Lower bounds for multicolor Ramsey numbers
Webb13 sep. 2024 · New lower bounds on the size-Ramsey number of a path. Deepak Bal, Louis DeBiasio. We prove that for all graphs with at most edges there exists a 2-coloring of the … Webb29 maj 2024 · Ramsey numbers lower bound Asked 3 years, 9 months ago Modified 3 years, 9 months ago Viewed 221 times 0 I have been given the following information, ( n k) 2 1 − ( k 2) < 1 t h e n R ( k, k) > n. Now I wish to show that for K ≥ 3 R ( k, k) ≥ 2 0.5 k Not sure where to start. combinatorics graph-theory ramsey-theory Share Cite Follow hear that noah
An improved lower bound for multicolor Ramsey numbers and the …
Webb25 feb. 2013 · Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange WebbAbstract. The multicolor Ramsey number R r ( H) is defined to be the smallest integer n = n ( r) with the property that any r -coloring of the edges of the complete graph K n must result in a monochromatic subgraph of K n isomorphic to H. It is well known that 2 rm < R r ( C2 m +1 )<2 ( r +2)! m and R r ( C2 m )≥ ( r −1) ( m −1)+1. Webb6. Multicolor Graph Ramsey Numbers 42 6.1 Bounds for classical numbers 42 6.2 General results for complete graphs 44 6.3 Cycles 46 6.4 Paths, paths versus other graphs 51 6.5 Special cases 53 6.6 General results for special graphs 54 6.7 General results 55 7. Hypergraph Ramsey Numbers 57 7.1 Values and bounds for numbers 57 7.2 Cycles and … mounted wanderers