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:

Keywords

• linear space,projective plane,complete graph

References

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