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....

A graph G is hypohamiltonian if G is non-hamiltonian and G − v is hamiltonian for every v ∈ V (G). In the following, every graph is assumed to be hypohamiltonian. Aldred, Wormald, and McKay gave a list of all graphs of order at most 17. In this article, we present an algorithm to generate all graphs of a given order and apply it to prove that there exist exactly 14 graphs of order 18 and 34 gra...

Let S ⊂ R be a set of n point sites, where each s ∈ S has an associated radius rs > 0. The disk graph D(S) of S is the graph with vertex set S and an edge between two sites s and t if and only if |st| ≤ rs + rt, i.e., if the disks with centers s and t and radii rs and rt, respectively, intersect. Disk graphs are useful to model sensor networks. We study the problems of finding triangles and of ...

The Girth-Chromatic number theorem is a theorem from graph theory, stating that graphs with arbitrarily large girth and chromatic number exist. We formalize a probabilistic proof of this theorem in the Isabelle/HOL theorem prover, closely following a standard textbook proof and use this to explore the use of the probabilistic method in a theorem prover.

We show that a planar graph with girth at least 20t−2 3 has circular chromatic number at most 2+ 1t , improving earlier results. This follows from a general result establishing homomorphisms into special targets for graphs with given girth and given maximum average degree. Other applications concern oriented chromatic number and homomorphisms into mixed graphs with colored edges.

The relation between the girth and the error correction capability of column-weight-three LDPC codes is investigated. Specifically, it is shown that the Gallager A algorithm can correct g/2 − 1 errors in g/2 iterations on a Tanner graph of girth g ≥ 10.

data on body weight and body measurements (body length, height at withers, chest girth and paunch girth) of adult kilakarsal sheep have been collected from 124 adult animals managed at the farmers filed in tirunelveli districts of tami nadu, india to estimate the body weight from body measurements. the data were subjected to standard statistical analysis using spss software and linear regressio...

This works presents a formalization of the Girth-Chromatic number theorem in graph theory, stating that graphs with arbitrarily large girth and chromatic number exist. The proof uses the theory of Random Graphs to prove the existence with probabilistic arguments and is based on [1].

The problem of colouring the square of a graph naturally arises in connection with the distance labelings, which have been studied intensively. We consider this problem for sparse subcubic graphs and show that the choosability χ`(G 2) of the square of a subcubic graph G of maximum average degree d is at most four if d < 24/11 and G does not contain a 5-cycle, χ`(G 2) is at most five if d < 7/3 ...