The Zarankiewicz number z(s, m) is the maximum number of edges in a subgraph of K(s, s) that does not contain K(m, m) as a subgraph. The bipartite Ramsey number b(m, n) is the lea...
Wayne Goddard, Michael A. Henning, Ortrud R. Oelle...
The Ramsey number r(H, Kn) is the smallest positive integer N such that every graph of order N contains either a copy of H or an independent set of size n. The Tur´an number ex(m,...
Eroh and Oellermann defined BRR(G1, G2) as the smallest N such that any edge coloring of the complete bipartite graph KN,N contains either a monochromatic G1 or a multicolored G2....
For two given graphs F and H, the Ramsey number R(F, H) is the smallest positive integer p such that for every graph G on p vertices the following holds: either G contains F as a ...
In the online F-avoidance edge-coloring game with r colors, a graph on n vertices is generated by at each stage randomly adding a new edge. The player must color each new edge as ...