—The n-dimensional augmented cube, denoted as AQ n , a variation of the hypercube, possesses some properties superior to those of the hypercube. In this paper, we show that every vertex in AQ n lies on a fault-free cycle of every length from 4 to 2 n , even if there are up to 2n  3 link faults. We also show that this result is optimal. I. INTRODUCTION A graph G is a triple consisting of a vert...

In 4] it is conjectured that all diregular c-partite tournaments, with c 4, are pan-cyclic. In this paper we show that all diregular c-partite tournaments, with c 5, are in fact vertex-pancyclic.

Choudum and Sunitha [Networks 40 (2002) 71–84] proposed the class of augmented cubes as a variation of hypercubes and showed that augmented cubes possess several embedding properties that the hypercubes and other variations do not possess. Recently, Hsu et al. [Information Processing Letters 101 (2007) 227–232] showed that the ndimensional augmented cube AQn, n 2, is weakly geodesic-pancyclic, ...

Bondy proved that an n-vertex simple Hamiltonian graph with at least n2/4 edges has cycles of every length unless it is isomorphic to Kn/2,n/2. This paper considers finding circuits of every size in GF (q)-representable matroids with large numbers of elements. A consequence of the main result is that a rank-r simple binary matroid with at least 2r−1 elements has circuits of all sizes or is isom...

A tournament is an orientation of a complete graph and a multipartite or c-partite tournament is an orientation of a complete c-partite graph. If D is a digraph, then let d + (x) be the outdgree and d ? (x) the indegree of the vertex x in D. The minimum (maximum) out-degree and the minimum (maximum) indegree of D are denoted by + ((+) and ? ((?), respectively. In addition, we deene = minf + ; ?...