Accession Number:

AD0739717

Title:

Shortness Exponents of Families of Graphs.

Descriptive Note:

Technical rept.,

Corporate Author:

WASHINGTON UNIV SEATTLE DEPT OF MATHEMATICS

Personal Author(s):

Report Date:

1972-04-01

Pagination or Media Count:

29.0

Abstract:

Let vG denote the number of vertices of a graph G and hG the maximal length of a simple circuit in G. A number alpha is a shortness exponent for a family G of graphs provided there exists a real beta and a sequence G sub n of graphs in G such that V sub n vG sub n approaches infinity for n to infinity and hG sub n or betav sub n sup alpha. Ten years ago the author and T. S. Motzkin established that alpha 1 - 2 sup -17 is a shortness exponent for the family of all 3-connected, 3-valent planar graphs. In the present report the author obtains strengthenings and generalizations of this result and of results of Moon and Moser, Walther, Jucovic and others. Author

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE