Cover: A Characterization of Clique Graphs

A Characterization of Clique Graphs

Published 1969

by Fred S. Roberts, J. H. Spencer

Purchase Print Copy

 Format Price
Add to Cart Paperback28 pages $20.00

A graph-theoretic discussion following up a recent paper in which Hamelink obtains an interesting sufficient condition for a graph to be a clique graph. In the present study related conditions are given that are necessary as well as sufficient. As an application of the result, it is shown that Hamelink's condition is also necessary in certain special cases and that here it can be greatly simplified. As another application, certain theorems are derived that are useful in practice in reducing the question of whether certain smaller or simpler graphs are clique graphs. Next, the clique graph results are related to some work of Fulkerson and Gross (RM-3984) on interval graphs and the consecutive 1's property. Finally, there are some remarks, motivated by the clique graph results, on graphs with no independent cut sets.

This report is part of the RAND research memorandum series. The Research Memorandum was a product of RAND from 1948 to 1973 that represented working papers meant to report current results of RAND research to appropriate audiences.

This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit www.rand.org/pubs/permissions.

RAND is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.