On size multipartite Ramsey numbers for stars versus paths and cycles

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 .

Size multipartite Ramsey numbers for stripes versus small cycles

For simple graphs G1 and G2, the size Ramsey multipartite number mj(G1, G2) is defined as the smallest natural number s such that any arbitrary two coloring of the graph Kj×s using the colors red and blue, contains a red G1 or a blue G2 as subgraphs. In this paper, we obtain the exact values of the size Ramsey numbers mj(nK2, Cm) for j ≥ 2 and m ∈ {3, 4, 5, 6}.

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 ...

Size Multipartite Ramsey Numbers for K4-e Versus all Graphs up to 4 Vertices

1 7 O ct 2 01 7 Projective planes and set multipartite Ramsey numbers for C 4 versus star Claudia

Set multipartite Ramsey numbers were introduced in 2004, generalizing the celebrated Ramsey numbers. Let C4 denote the four cycle and let K1,n denote the star on n + 1 vertices. In this paper we investigate bounds on C4−K1,n set multipartite Ramsey numbers. Relationships between these numbers and the classical C4−K1,n Ramsey numbers are explored. Then several near-optimal or exact classes are d...