Lower bounds of the size multipartite Ramsey numbers mj(Pn,Kj×b)

A Size Multipartite Ramsey Problem Involving the Claw Graph

“…Given any two colouring of the edges of the graph K = K j×s , let the red and blue subgraphs of [3,7,9]) and row 7 and row 10 follows from Jayawardene et al (see [5,6]).…”

“…Given any two graphs G and H, the classical Ramsey number (see [2,4,7,8]) r(H,G) is defined as the smallest positive integer n such that K n → (H,G). A natural generalization of the popular classical Ramsey number is the size multipartite Ramsey number which was introduced a few decades ago (see [1,9]). The balanced complete multipartite graph denoted by K=K j×s is defined as a graph consisting of j uniform partite sets s, where The size Ramsey multipartite number m j (K 1,3 ,G) is defined as the smallest natural number s such that K j×s → (K 1,3 ,G).…”

Size multipartite Ramsey numbers for small paths versus books

“…More precisely, given j ≥ 2, for graphs G and H, the size Ramsey multipartite number m j (G, H) is defined as the smallest natural number t such that any blue red coloring of the edges of the graph K j×t , necessarily contains a red G or a blue H as subgraphs. Up to now a few classes of such Ramsey Numbers have been investigated by Syafrizal Sy, Baskaro et al (see [8] and [9]). In this paper, motivated by the work done by Rousseau et al on Book Ramsey numbers we try to investigate the nature of size Ramsey multipartite numbers for small paths verses books.…”

Size Multipartite Ramsey Numbers for Small Paths Versus Stripes

“…. These bipartite Ramsey numbers have been explored extensively in the last decade (see [2,3,4,5,6] [1,10]) in the last decade. However, not much papers have been published in this area except for paths and cycles versus some small classes of graphs.…”

“…However, not much papers have been published in this area except for paths and cycles versus some small classes of graphs. (see [1,10]). …”