Cover: Intersection Graphs of Families of Convex Sets with Distinguished Points.

Intersection Graphs of Families of Convex Sets with Distinguished Points.

Published 1969

by W. F. Ogden, Fred S. Roberts

Purchase Print Copy

 Format Price
Add to Cart Paperback $20.00

Collection of intersection graphs C prime (n) is defined as all finite graphs (V, E) in which there is an assignment to each x in V of a set C(x) in a family of convex sets so that for x not equal to y, (x, y) is a member of E if and only if f(x) is a member of C(y). A graph in C prime (1) is defined as an indifference graph if each C(x) can be taken as a closed unit interval and f(x) is its midpoint. Given these definitions, two theorems are proven: first, that C prime (1) equals the class of indifference graphs, which equals the class of unit interval graphs and, second, that every graph is in C prime (2). 4 pp. Refs. (KB)

This report is part of the RAND paper series. The paper was a product of RAND from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review.

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

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.