Intersection Graphs of Families of Convex Sets with Distinguished Points.
ResearchPublished 1969
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)
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- Copyright: RAND Corporation
- Availability: Available
- Year: 1969
- Print Format: Paperback
- Paperback Price: $20.00
- Document Number: P-4094
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Ogden, W. F. and Fred S. Roberts, Intersection Graphs of Families of Convex Sets with Distinguished Points. RAND Corporation, P-4094, 1969. As of September 14, 2024: https://www.rand.org/pubs/papers/P4094.html
Ogden, W. F. and Fred S. Roberts, Intersection Graphs of Families of Convex Sets with Distinguished Points. Santa Monica, CA: RAND Corporation, 1969. https://www.rand.org/pubs/papers/P4094.html. Also available in print form.
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