Paunch contents are the recalcitrant, lignocellulose-rich, partially-digested feed present in rumen of ruminant animals. Cattle forage Europe is primarily from perennial and Italian ryegrasses and/or white clover, so paunch forage-fed cattle enriched these feedstuffs. Globally, due to its underutilisation, potential energy annually represents an loss 23,216,548,750–27,804,250,000 Megajoules (MJ...

Let G be an r-regular graph of order n and independence number α(G). We show that if G has odd girth 2k + 3 then α(G) ≥ n1−1/kr1/k . We also prove similar results for graphs which are not regular. Using these results we improve on the lower bound of Monien and Speckenmeyer, for the independence number of a graph of order n and odd girth 2k + 3. AMS Subject Classification. 05C15 §

It was proved in [Z. Dvořàk, D. Kràl, P. Nejedlỳ, R. Škrekovski, Coloring squares of planar graphs with girth six, European J. Combin. 29 (4) (2008) 838–849] that every planar graph with girth g ≥ 6 and maximum degree ∆ ≥ 8821 is 2-distance (∆ + 2)-colorable. We prove that every planar graph with g ≥ 6 and∆ ≥ 18 is 2-distance (∆+ 2)-colorable. © 2009 Elsevier B.V. All rights reserved.

Motivated by the work of Nešetřil and Rödl on “Partitions of vertices”, we are interested in obtaining some quantitative extensions of their result. In particular, given a natural number r and a graph G of order m with odd girth g, we show the existence of a graph H with odd girth at least g and order that is polynomial in m such that every r-coloring of the vertices of H yields a monochromatic...

Here we present an overview of various techniques performed concomitantly during penile prosthesis surgery to enhance penile length and girth. We report on the technique of ventral phalloplasty and its outcomes along with augmentation corporoplasty, suprapubic lipectomy, suspensory ligament release, and girth enhancement procedures. For the serious implanter, outcomes can be improved by combini...

let r be a fnite commutative ring and n(r) be the set of non unit elements of r. the non unit graph of r, denoted by gamma(r), is the graph obtained by setting all the elements of n(r) to be the vertices and defning distinct vertices x and y to be adjacent if and only if x - yin n(r). in this paper, the basic properties of gamma(r) are investigated and some characterization results regarding co...

In this paper, we propose a novel method for constructing quasi-cyclic low-density parity check (QC-LDPC) codes based row division method which can guarantee a concentrated node degree distribution with large girth. The main advantage is that large girth QC-LDPC codes can be easily constructed with a variety of block lengths and rates. Simulation results show that the proposed codes perform sig...

Design of binary LDPC codes with very low error floors is still a significant problem. Progressive Edge-Growth (P.E.G) original is a well known algorithm for constructing bipartite graphs with good girth properties. In this paper, we propose a characterization of the trapping set TS(5,3) and a cost function in P.E.G that allows to build regular girth 8 LDPC codes free of TS(5,3). We illustrate ...

We show that a graph of girth greater than 6 log k + 3 and minimum degree at least 3 has a minor of minimum degree greater than k. This is best possible up to a factor of at most 9/4. As a corollary, every graph of girth at least 6 log r + 3 log log r + c and minimum degree at least 3 has a Kr minor.