Set and size multipartite Ramsey numbers for stars

Multipartite Ramsey Numbers of Union of Stars

“…In 2004, Burger and Van Vuuren [1,2] introduced the notion of set multipartite Ramsey number and size multipartite Ramsey number as variations of the classical Ramsey number. The extension to many colors is established in [3], and the extension in a more general setting is presented in [9,12]. For c ≥ 2, s ≥ 1, denote by K c×s the complete multipartite graph with c partite sets, each of which contains s vertices.…”

“…In 2018, Perondi and Carmelo [9] completely determined the set and size multipartite Ramsey number of stars. Their results are presented in Theorems 1.1 and 1.2.…”

Some results on the multipartite Ramsey numbers m(C3,C,n1K2,n2K2,…,nK2)

“…Burgeet et al have done a research on the value of , under the condition which G and H are both complete multipartite graphs in [6] . Recently, the exact value of was calculated for certain graph classes, see [7] , [8] , [9] alongside related references, which normally can be boosted to various colors, see [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] . The multipartite Ramsey number in case that G is considered as a path or a cycle including n vertices and , has been studied in [14] .…”

The Size, Multipartite Ramsey Numbers for nK2 Versus Path–Path and Cycle

“…The size of the multipartite Ramsey numbers of small paths versus certain classes of graphs have been studied in [8][9][10]. The size of the multipartite Ramsey numbers of stars versus certain classes of graphs have been studied in [11,12]. In [13,14], Burger, Stipp, Vuuren, and Grobler investigated the multipartite Ramsey numbers m j (G 1 , G 2 ), where G 1 and G 2 are in a completely balanced multipartite graph, which can be naturally extended to several colors.…”