Chris D. Godsil

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A k X n Latin rectangle is a k X n matrix with entries from {1,2,.. . , n} such that no entry occurs more than once in any row or column. (Thus each row is a permutation of the integers 1,2,..., n.) Let L(k, n) be the number of k x n Latin rectangles. An outstanding problem is to determine the asymptotic value of L(k, n) as n —• oo, with k bounded by a(More)
The number of vertices missed by a maximum matching in a graph G is the multiplicity of zero as a root of the matchings polynomial μ(G,x) of G, and hence many results in matching theory can be expressed in terms of this multiplicity. Thus, if mult(θ,G) denotes the multiplicity of θ as a zero of μ(G,x), then Gallai’s lemma is equivalent to the assertion that(More)
Let G be a group acting as a regular permutation group on the set V = {I, ... , g}. Let C be a subset of G\L, where L denotes the identity element of G. The Cayley digraph X of G with respect to C has vertex set V and if a, {3 E G then there is an arc from la to 1{3 iff (3a -1 E C. X will be an (undirected) graph iff C is inverse-closed, that is, if y E C(More)
The width of a subset C of the vertices of a distance-regular graph is the maximum distance which occurs between elements of C. Dually, the dual width of a subset in a cometric association scheme is the index of the “last” eigenspace in the Q-polynomial ordering to which the characteristic vector of C is not orthogonal. Elementary bounds are derived on(More)