Recently, Souza introduced blowup Ramsey numbers as a generalization of bipartite numbers. For graphs $G$ and $H$, say $G\overset{r}{\longrightarrow} H$ if every $r$-edge-coloring contains monochromatic copy $H$. Let $H[t]$ denote the $t$-blowup Then number $G,H,r,$ $t$ is defined minimum $n$ such that $G[n] \overset{r}{\longrightarrow} H[t]$. proved upper lower bounds on are exponential in $t$...

for a graph g, let d(g) be the set of all strong orientations of g. the orientationnumber of g is min {d(d) |d belongs to d(g)}, where d(d) denotes the diameterof the digraph d. in this paper, we determine the orientation number for some subgraphs of complete bipartite graphs.

In this paper, we study an analogue of size-Ramsey numbers for vertex colorings. For a given number of colors r and a graph G the vertex size-Ramsey number of G, denoted by R̂v(G, r), is the least number of edges in a graph H with the property that any r-coloring of the vertices of H yields a monochromatic copy of G. We observe that Ωr(∆n) = R̂v(G, r) = Or(n ) for any G of order n and maximum deg...