Leave Graphs of Small Maximal Partial Triple Systems

Charles J. Colbourn1, Rudolf A. Mathon2
1 Department of Computer Science, University of Waterloo, Waterloo, Ontario, N2L 3G1 CANADA
2Department of Computer Science, University of Toronto, Toronto, Ontario, M5S 1Al1 CANADA

Abstract

All graphs meeting the basic necessary conditions to be the leave graph of a maximal partial triple system with at most thirteen elements are generated. A hill-climbing algorithm is developed to determine which of these candidates are in fact leave graphs. Improved necessary conditions for a graph to be a leave graph are developed.