Hypergraphic matroids were de ned by Lorea as generalizations of graphic matroids. We show that the minimum cut (co-girth) of a multiple of a hypergraphic matroid can be computed in polynomial time. It is well-known that the size of the minimum cut (co-girth) of a graph can be computed in polynomial time. For connected graphs, this is equivalent to computing the co-girth of the circuit matroid....

Girth pairs were introduced by Harary and Kovács [Regular graphs with given girth pair, J. Graph Theory 7 (1983) 209–218]. The odd girth (even girth) of a graph is the length of a shortest odd (even) cycle. Let g denote the smaller of the odd and even girths, and let h denote the larger. Then (g, h) is called the girth pair of the graph. In this paper we prove that a graph with girth pair (g, h...

A method to construct girth-12 (3,L) quasi-cyclic lowdensity parity-check (QC-LDPC) codes with all lengths larger than a certain given number is proposed, via a given girth-12 code subjected to some constraints. The lengths of these codes can be arbitrary integers of the form LP, provided that P is larger than a tight lower bound determined by the maximal element within the exponent matrix of t...

It is well known that 3–regular graphs with arbitrarily large girth exist. Three constructions are given that use the former to produce non-Hamiltonian 3–regular graphs without reducing the girth, thereby proving that such graphs with arbitrarily large girth also exist. The resulting graphs can be 1–, 2– or 3–edge-connected depending on the construction chosen. From the constructions arise (nai...

An evaluation of reproductive performance, behavior, immunity and ergonomics was conducted for two common sow housing systems: the girth tether and crate. Littermate Yorkshire × Landrace gilts were randomly assigned to either the crate or girth tether system and they remained in that treatment for two consecutive pregnancies and lactations. A total of 171 matings resulted in 141 litters (82.4% ...

INTRODUCTION Current girth augmentation techniques rely either on liposuction/injection or on the use of dermal fat grafts. These procedures have serious disadvantages, including regression in gained size, deformities, irregular contour, and asymmetry. Ideally, the augmentation technique should ensure durability and symmetry. This case report describes the first application of a flap (superfici...

We describe two computational methods for the construction of cubic graphs with given girth. These were used to produce two independent proofs that the (3, 9)-cages, defined as the smallest cubic graphs of girth 9, have 58 vertices. There are exactly 18 such graphs. We also show that cubic graphs of girth 11 must have at least 106 vertices and cubic graphs of girth 13 must have at least 196 ver...

We describe two new algorithms for the generation of all non-isomorphic cubic graphs with girth at least k ≥ 5 which are very efficient for 5 ≤ k ≤ 7 and show how these algorithms can be efficiently restricted to generate snarks with girth at least k. Our implementation of these algorithms is more than 30, respectively 40 times faster than the previously fastest generator for cubic graphs with ...

The body measurements of 433 young Dorper rams participating in the Free State and Northern Cape veld-ram projects were correlated with their production performance. These measurements included a selection index, body weight (kg), average daily gain (g/day) and scrotal circumference (cm). The performance of the animals in the two projects compared well, although the means in the Free State proj...