ABSTRACT
The n×n-chessboard B n many times has been the object of problems in combinatorial geometry. Here we will consider the set of sides of the squares of B n . Then we may ask, for example, for the largest n for which it is possible to remove vertex disjoint edges from B n such that no path of given length remains. More general, we partition the set of all sides into two color classes and then ask for the existence of certain monochromatic configurations. If B n is interpreted as the graph B n with the vertex points of the squares as vertices, and with the sides as edges then we will ask for the minimum number r=r (G,H) such that every two-coloring (green and red) of the edges of B r contains a given subgraph G in green or a given subgraph H in red. That is, we ask for a Ramsey like number where instead of the complete graphs K n the chessboard graphs B n serve as ‘host graphs’. In the literature, besides the classical case of K n [4], for example, complete bipartite graphs [1], cube graphs [2] and octahedron graphs [3] are discussed as other sequences of host graphs.
