Shortness Exponents of Families of Graphs.
WASHINGTON UNIV SEATTLE DEPT OF MATHEMATICS
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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
- Theoretical Mathematics