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Embedding the complement of two lines in a finite projective plane

Published online by Cambridge University Press:  09 April 2009

Jim Totten
Jim Totten
Affiliation:
Mathematisches Institutder Universität Tübingen7400 Tübingen 1Auf der Morgenstelle 10West Germany.
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In this paper we use a result from graph theory on the characterization of the line graphs of the complete bigraphs to show that if n is any integer ≥ 2 then any finite linear space having p = n2 − n or p = n2 − n + 1 points, of which at least n2 − n have degree n + 1, and q ≤ n2 + n − 1 lines is embeddable in an FPP of order n unless n = 4. If n = 4 there is only one possible exception for each of the two values of p, and for p = n2 − n, this exception can be embedded in the FPP of order 5.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 22 , Issue 1 , August 1976 , pp. 27 - 34
Copyright
Copyright © Australian Mathematical Society 1976

References

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