Vertices Missed by Longest Paths or Circuits.

Abstract

Let G denote a graph with v(G) vertices, and let c(G) and p(G) denote the maximal numbers of vertices contained in any simple circuit or path in G. The author denotes by c(j,k) (p(j,k)) the greatest lower bounds of v(G) where G is a k-connected graph such that for every choice of j vertices of G there exists in G a simple circuit (path) with c(G) (p(G)) vertices that misses the j chosen vertices. Analogously defined numbers with G restricted to planar graphs are denoted by (c sub 0)(j,k) and (p sub 0)(j,k). Extending various known results it is established that (c sub 0)(1,3) < or = 124, (p sub 0)(1,3) < or = 484, c(2.3) < or = 90 and p(2.3) < or = 324. (Modified author abstract)

Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1973
Accession Number
AD0764091

Entities

People

  • Branko Grunbaum

Organizations

  • University of Washington

Tags

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.