Size Ramsey results for paths versus stars

On size multipartite Ramsey numbers for stars versus paths and cycles

Let Kl×t be a complete, balanced, multipartite graph consisting of l partite sets and t vertices in each partite set. For given two graphs G1 and G2, and integer j ≥ 2, the size multipartite Ramsey number mj(G1, G2) is the smallest integer t such that every factorization of the graph Kj×t := F1 ⊕ F2 satisfies the following condition: either F1 contains G1 or F2 contains G2. In 2007, Syafrizal e...

Size Ramsey Numbers of Stars versus 4-Chromati Graphs

Size Multipartite Ramsey Numbers for Small Paths Versus Stripes

For graphs G and H, the size balanced multipartite Ramsey number ) , ( H G m j is defined as the smallest positive integer s such that any arbitrary two red/blue coloring of the graph s j K × forces the appearance of a red G or a blue H . In this paper we find the exact values of the multipartite Ramsey numbers ) , ( 2 3 nK P m j and ) , ( 2 4 nK P m j .

Ramsey numbers of ordered graphs

An ordered graph G< is a graph G with vertices ordered by the linear ordering <. The ordered Ramsey number R(G<, c) is the minimum number N such that every ordered complete graph with c-colored edges and at least N vertices contains a monochromatic copy of G<. For unordered graphs it is known that Ramsey numbers of graphs with degrees bounded by a constant are linear with respect to the number ...

The Ramsey Numbers for Disjoint Union of Stars

The Ramsey number for a graph G versus a graph H, denoted by R(G,H), is the smallest positive integer n such that for any graph F of order n, either F contains G as a subgraph or F contains H as a subgraph. In this paper, we investigate the Ramsey numbers for union of stars versus small cycle and small wheel. We show that if ni ≥ 3 for i = 1, 2, . . . , k and ni ≥ ni+1 ≥ √ ni − 2, then R( ∪k i=...