Ramsey numbers in complete balanced multipartite graphs. Part II: Size numbers

Ramsey numbers in complete balanced multipartite graphs. Part I: Set numbers

The notion of a graph theoretic Ramsey number is generalised by assuming that both the original graph whose edges are arbitrarily bi–coloured and the sought after monochromatic subgraphs are complete, balanced, multipartite graphs, instead of complete graphs as in the classical definition. We previously confined our attention to diagonal multipartite Ramsey numbers. In this paper the definition...

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 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 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...