
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) : Gruenbaum,Branko
Report Date : APR 1972
Pagination or Media Count : 29
Abstract : Let v(G) denote the number of vertices of a graph G and h(G) 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 = v(G sub n) approaches infinity for n to infinity and h(G sub n) < or = beta(v 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 3connected, 3valent 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)
Descriptors : (*GRAPHICS, THEOREMS), MAPPING(TRANSFORMATIONS), CIRCUITS, TOPOLOGY
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE