Centre for Discrete and Applicable Mathematics
	CDAM Research Report, LSE-CDAM-99-05 June 1999

Abstract

An explicit formula for the chromatic polynomial of the  3 x n  toroidal square lattice graph is obtained. The formula is expressed in terms of the eigenvalues of a matrix  T,  known as the compatibility matrix. The two key techniques are:  (i) a sieve formula for the action of  T,  and (ii) the construction of certain invariant subspaces of  T.  Both techniques can be generalised.

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