Learn More
We say a digraph G is hyperhamiltonian if there is a spanning closed walk in G which passes through one vertex exactly twice and all others exactly once. We show the cartesian product Zg x Zb of t w o directed cycles is hyperhamiltonian if and only if there are positive integers m and n with ma + nb = ab + 1 and gcd(m, n) = 1 or 2, We obtain a similar(More)
  • D Carter, G Keller, E Paige, Dave Witte, Morris
  • 2005
We present unpublished work of on bounded generation in special linear groups. Let n be a positive integer, and let A = O be the ring of integers of an algebraic number field K (or, more generally, let A be a localization OS −1). If n = 2, assume that A has infinitely many units. We show there is a finite-index subgroup H of SL(n, A), such that every matrix(More)
We show that the Cartesian product Za x Zb of two directed cycles is hypo-Hamiltonian (Hamiltonian) if and only if there is a pair of relatively prime positive integers m and n with ma + nb = ab-1 (ma + nb = ab). The result for hypo-Hamiltonian is new; that for Hamiltonian is known. These are special cases of the fact that there is a simple circuit of(More)
We construct infinitely many connected, circulant digraphs of outdegree three that have no hamiltonian circuit. All of our examples have an even number of vertices, and our examples are of two types: either every vertex in the digraph is adjacent to two diametrically opposite vertices, or every vertex is adjacent to the vertex diametrically opposite to(More)
It has been shown that there is a Hamilton cycle in every connected Cayley graph on any group G whose commutator subgroup is cyclic of prime-power order. This note considers connected, vertex-transitive graphs X of order at least 3, such that the automorphism group of X contains a vertex-transitive subgroup G whose commutator subgroup is cyclic of(More)