# Upper bounds for the connective constant of self-avoiding walks

#### by

## Sven Erick Alm

#### Uppsala University

##### In Combinatorics, Probability and Computing (1993) 2, 115-136

### Abstract

We present a method for obtaining upper bounds for the connective constant of
self-avoiding walks. The method works for a large class of lattices,
including all that have been studied in connection with self-avoiding walks.

The bound is obtained as the largest eigenvalue of a certain matrix.
Numerical application of the method has given improved upper bounds for all
lattices studied, e.g. 2.696 for the square lattice,
4.278 for the triangular lattice and 4.756 for the simple
cubic lattice.

Research supported by the Swedish Natural Science Research
Council.
1995-02-06, Sven Erick Alm, sea@math.uu.se