EMBEDDING THE COMPLEMENT OF A COMPLETE GRAPH IN A FINITE PROJECTIVE PLANE

Abstract

Let S = (P;L) be a non-trivial regular nite linear space with v points, v + k lines, k 3: We show that if S contains at least 􀀀k 2 lines of size b(p) 􀀀 2 and one line size b(p) for some point p, then S is embeddable in a unique projective plane of order b(p) 􀀀 1 and 􀀀 s is a complete graph of order k ; where b(p) 4 for some point p: