Size Multipartite Ramsey Numbers for Small Paths Versus Stripes

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 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}.

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

The Ramsey numbers of large trees versus wheels

For two given graphs G1 and G2, the Ramseynumber R(G1,G2) is the smallest integer n such that for anygraph G of order n, either $G$ contains G1 or the complementof G contains G2. Let Tn denote a tree of order n andWm a wheel of order m+1. To the best of our knowledge, only R(Tn,Wm) with small wheels are known.In this paper, we show that R(Tn,Wm)=3n-2 for odd m with n>756m^{10}.

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...