No abstract

No abstract

For the maximum number f ( n ) of edges in a C4-free subgraph of the n-dimensional cube-graph 0, w e prove f(n) 2 i ( n + f i ) 2 " -' for n = 4f, and f ( n ) 2 i ( n + 0.9,h)2"-' for all n 2 9. This disproves one version of a conjecture of P. Erdos. 0 1995 John Wiley & Sons, Inc.

No abstract

For all n > d there exist n points in the Euclidean space E d such that not all points are in a hyperplane and all mutual distances are integral. It is proved that the minimum diameter of such integral point sets has an upper bound of 2 cl°gnl°gl°gn.