The size-Ramsey number of 3-uniform tight paths
نویسندگان
چکیده
منابع مشابه
The Ramsey Number of Loose Paths in 3-Uniform Hypergraphs
Recently, asymptotic values of 2-color Ramsey numbers for loose cycles and also loose paths were determined. Here we determine the 2-color Ramsey number of 3-uniform loose paths when one of the paths is significantly larger than the other: for every n > ⌊ 5m 4 ⌋ , we show that R(P n,P m) = 2n + ⌊m + 1 2 ⌋ .
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Let C (3) n denote the 3-uniform tight cycle, that is the hypergraph with vertices v1, . . . , vn and edges v1v2v3, v2v3v4, . . . , vn−1vnv1, vnv1v2. We prove that the smallest integer N = N(n) for which every red-blue coloring of the edges of the complete 3-uniform hypergraph with N vertices contains a monochromatic copy of C (3) n is asymptotically equal to 4n/3 if n is divisible by 3, and 2n...
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Let H = (V, E) be an r-uniform hypergraph. For each 1 ≤ s ≤ r − 1, an spath P n in H of length n is a sequence of distinct vertices v1, v2, . . . , vs+n(r−s) such that {v1+i(r−s), . . . , vs+(i+1)(r−s)} ∈ E(H) for each 0 ≤ i ≤ n − 1. Recently, the Ramsey number of 1-paths and 1-cycles in uniform hypergraphs attracted a lot of attention. The asymptotic value of R(P n ,P 3,1 n ) was first determi...
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The size-Ramsey number of a graph G is the smallest number of edges in a graph Γ with the Ramsey property for G, that is, with the property that any colouring of the edges of Γ with two colours (say) contains a monochromatic copy of G. The study of size-Ramsey numbers was proposed by Erdős, Faudree, Rousseau, and Schelp in 1978, when they investigated the size-Ramsey number of certain classes o...
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ژورنال
عنوان ژورنال: Advances in Combinatorics
سال: 2021
ISSN: 2517-5599
DOI: 10.19086/aic.24581