We investigate the basic interplay between the small k-valent vertex-transitive graphs of girth g and the (k, g)-cages, the smallest k-valent graphs of girth g. We prove the existence of k-valent Cayley graphs of girth g for every pair of parameters k ≥ 2 and g ≥ 3, improve the lower bounds on the order of the smallest (k, g) vertex-transitive graphs for certain families with prime power girth,...

Homomorphisms between graphs are studied as a generalization of colorings and of chromatic number. We investigate here homomorphisms from orienta-tions of undirected planar graphs to graphs (not necessarily planar) containing as few digons as possible. We relate the existence of such homomorphisms to girth and it appears that these questions remain interesting even under large girth assumption ...

The well-known Moore bound M(k, g) serves as a universal lower bound for the order of k-regular graphs of girth g. The excess e of a k-regular graph G of girth g and order n is the difference between its order n and the corresponding Moore bound, e = n −M(k, g). We find infinite families of parameters (k, g), g > 6 and even, for which we show that the excess of any k-regular graph of girth g is...

Girth weld cracking is one of the main failure modes in oil and gas pipelines; girth weld cracking inspection has great economic and social significance for the intrinsic safety of pipelines. This paper introduces the typical girth weld defects of oil and gas pipelines and the common nondestructive testing methods, and systematically generalizes the progress in the studies on technical principl...

BACKGROUND Given an emerging concern for juvenile overweight and obesity, even in populations of developing countries, techniques to assess central obesity, such as abdominal circumference (AC), are of increasing interest. OBJECTIVE To compare two procedures for measuring AC in schoolchildren from a convenience sample of middle-class, urban children aged 72 to 131 months in Guatemala City. ...

Independent of whether natural mating or artificial insemination is used for breeding, libido (sex drive) is evidently crucial to reproductive competence in all male meat animal species. Breeding goat bucks vary in their levels of libido; therefore, there is a need for the development of a predictive standardized test for estimating sex drive. The objective of this study was to evaluate libido ...

We prove that every graph of minimum degree at least r and girth at least 186 contains a subdivision of Krþ1 and that for r5435 a girth of at least 15 suffices. This implies that the conjecture of Haj ! os that every graph of chromatic number at least r contains a subdivision of Kr (which is false in general) is true for graphs of girth at least 186 (or 15 if r5436). More generally, we show tha...

Let G = (V,E) be a graph of order p and size q. It is known that if G is super edge-magic graph then q ≤ 2p− 3. Furthermore, if G is super edge-magic and q = 2p− 3, then the girth of G is 3. It is also known that if the girth of G is at least 4 and G is super edge-magic then q ≤ 2p − 5. In this paper we show that there are infinitely many graphs which are super edge-magic, have girth 5, and q =...

For every r ∈ N, let θr denote the graph with two vertices and r parallel edges. The θr-girth of a graph G is the minimum number of edges of a subgraph of G that can be contracted to θr. This notion generalizes the usual concept of girth which corresponds to the case r = 2. In [Minors in graphs of large girth, Random Structures & Algorithms, 22(2):213–225, 2003], Kühn and Osthus showed that gra...

Large-girth quasi-cyclic LDPC codes have been experimentally evaluated for use in PMD compensation by turbo equalization for a 10 Gb/s NRZ optical transmission system, and observing one sample per bit. Net effective coding gain improvement for girth-10, rate 0.906 code of length 11936 over maximum a posteriori probability (MAP) detector for differential group delay of 125 ps is 6.25 dB at BER o...