A Hamiltonian path (cycle) of a graph is a simple path (cycle) which visits each vertex of the graph exactly once. The Hamiltonian path (cycle) problem is to determine whether a graph contains a Hamiltonian path (cycle). A graph is called Hamiltonian connected if there exists a Hamiltonian path between any two distinct vertices. Supergrid graphs were first introduced by us and include grid grap...

In a graph G, a k-container Ck(u, v) is a set of k disjoint paths joining u and v. A k-container Ck(u, v) is k ∗-container if every vertex of G is passed by some path in Ck(u, v). A graph G is k ∗-connected if there exists a k∗-container between any two vertices. An m-regular graph G is super-connected if G is k∗-connected for any k with 1 k m. In this paper, we prove that the recursive circula...

Food production needs to double, with minimum waste, if hunger and poverty is to be alleviated in South Africa. The condemnation of liver during meat inspection represents a huge waste of a protein food resource. This paper measures the quantity of liver condemned in three abattoirs in the Eastern Cape Province of South Africa and assesses the causes and the monetary loss associated with these ...

We show that if G = (V,E) is a 4-connected flat graph, then any real symmetric V × V matrix M with exactly one negative eigenvalue and satisfying, for any two distinct vertices i and j, Mij < 0 if i and j are adjacent, and Mij = 0 if i and j are nonadjacent, has the Strong Arnold Property: there is no nonzero real symmetric V ×V matrix X with MX = 0 and Xij = 0 whenever i and j are equal or adj...

In this article we introduce the notion of multi-Koszul algebra for the case of a locally finite dimensional nonnegatively graded connected algebra, as a generalization of the notion of (generalized) Koszul algebras defined by R. Berger for homogeneous algebras. This notion also extends and generalizes the one recently introduced by the author and A. Rey, which was for the particular case of al...

The routine measurement of direction-dependent reservoir rock properties like permeability often takes place along the axial direction of core samples. As permeability is a tensor property of porous materials, it should be fully described by a tensor matrix or by three main permeabilities in principal directions. Due to compaction, cementation, and other lithification processes, which take plac...