The Circular Dimension of a Graph.

R. B. Feinberg

Expert InsightsPublished 1970

A contribution to the abstract theory of graphs. A graph G is an ordered pair (V, I), where V is a nonempty collection of vertices and I is a reflexive and symmetric binary relation of adjacency on V. There is a collection of functions that maps each vertex of V into an arc on a fixed circle. The circular dimension of G is defined as the smallest integer m such that G has an m-arc intersection model. A graph is complete partite if its vertices can be partitioned into disjoint classes so that any 2 vertices from the same class are nonadjacent, while any 2 vertices from different classes are adjacent. This paper establishes that the maximum circular dimension of any complete partite graph having n vertices is the largest integer p such that 2 (exp p) + p is less than or equal to n + 1. 24 pp. Bibliog. (MW)

Document Details

  • Copyright: RAND Corporation
  • Availability: Web Only
  • Year: 1970
  • Pages: 24
  • Document Number: P-4489

Citation

Chicago Manual of Style

Feinberg, R. B., The Circular Dimension of a Graph. Santa Monica, CA: RAND Corporation, 1970. https://www.rand.org/pubs/papers/P4489.html.
BibTeX RIS

This publication is part of the RAND paper series. The paper series 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 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.