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In this paper, we consider a variant of Ramsey numbers which we call complementary Ramsey numbers $bar{R}(m,t,s)$. We first establish their connections to pairs of Ramsey $(s,t)$-graphs. Using the classification of Ramsey $(s,t)$-graphs for small $s,t$, we determine the complementary Ramsey numbers $bar{R}(m,t,s)$ for $(s,t)=(4,4)$ and $(3,6)$.
Given graphs $H_1, dots, H_t$, a graph $G$ is $(H_1, dots, H_t)$-Ramsey-minimal if every $t$-coloring of the edges of $G$ contains a monochromatic $H_i$ in color $i$ for some $iin{1, dots, t}$, but any proper subgraph of $G $ does not possess this pr
We estimate Ramsey numbers for bipartite graphs with small bandwidth and bounded maximum degree. In particular we determine asymptotically the two and three color Ramsey numbers for grid graphs. More generally, we determine asymptotically the two col
Finding exact Ramsey numbers is a problem typically restricted to relatively small graphs. The flag algebra method was developed to find asymptotic results for very large graphs, so it seems that the method is not suitable for finding small Ramsey nu
For an integer $qge 2$, a graph $G$ is called $q$-Ramsey for a graph $H$ if every $q$-colouring of the edges of $G$ contains a monochromatic copy of $H$. If $G$ is $q$-Ramsey for $H$, yet no proper subgraph of $G$ has this property then $G$ is called
A set of vertices $Xsubseteq V$ in a simple graph $G(V,E)$ is irredundant if each vertex $xin X$ is either isolated in the induced subgraph $langle Xrangle$ or else has a private neighbor $yin Vsetminus X$ that is adjacent to $x$ and to no other vert