منابع مشابه
Directed Ramsey number for trees
In this paper, we study Ramsey-type problems for directed graphs. We first consider the k-colour oriented Ramsey number of H, denoted by − →r (H, k), which is the least n for which every k-edgecoloured tournament on n vertices contains a monochromatic copy of H. We prove that − →r (T, k) ≤ ck|T |k for any oriented tree T . This is a generalisation of a similar result for directed paths by Chvát...
متن کاملThe tripartite Ramsey number for trees
We prove that for every ε > 0 there are α > 0 and n0 ∈ N such that for all n ≥ n0 the following holds. For any two-colouring of the edges of Kn,n,n one colour contains copies of all trees T of order k ≤ (3− ε)n/2 and with maximum degree ∆(T ) ≤ n. This answers a conjecture of Schelp.
متن کاملThe size-Ramsey number of trees
Given a graph G, the size-Ramsey number r̂(G) is the minimum number m for which there exists a graph F on m edges such that any two-coloring of the edges of F admits a monochromatic copy of G. In 1983, J. Beck introduced an invariant β(·) for trees and showed that r̂(T ) = Ω(β(T )). Moreover he conjectured that r̂(T ) = Θ(β(T )). We settle this conjecture by providing a family of graphs and an emb...
متن کاملThe Size-Ramsey Number of Trees
If G and H are graphs, let us write G → (H)2 if G contains a monochromatic copy ofH in any 2-colouring of the edges of G. The size-Ramsey number re(H) of a graph H is the smallest possible number of edges a graph G may have if G→ (H)2. Suppose T is a tree of order |T | ≥ 2, and let t0, t1 be the cardinalities of the vertex classes of T as a bipartite graph, and let ∆(T ) be the maximal degree o...
متن کاملRamsey numbers for trees
For n ≥ 5 let T ′ n denote the unique tree on n vertices with ∆(T ′ n) = n − 2, and let T ∗ n = (V, E) be the tree on n vertices with V = {v0, v1, . . . , vn−1} and E = {v0v1, . . . , v0vn−3, vn−3vn−2, vn−2vn−1}. In this paper we evaluate the Ramsey numbers r(Gm, T ′ n) and r(Gm, T ∗ n), where Gm is a connected graph of order m. As examples, for n ≥ 8 we have r(T ′ n, T ∗ n) = r(T ∗ n , T ∗ n) ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2019
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2018.12.006