The proof of the following theorem is the main result of this paper: If G is a 2k-regular graph that has a perfect 1-factorisation, then the line graph, L(G), of G is Hamilton decomposable. Consideration is given to Hamilton decompositions of L(K 2k ? F).

In this paper we show that the complete graph K 12 is not decomposable into three factors with diameter two, which completes the solution of the problem of decomposition of complete graph into three factors from which the rst one has diameter two and the other factors have nite diameters.

We establish concentration inequalities for Lipschitz functions of dependent random variables, whose dependencies are specified by forests. also give results decomposable functions, improving Janson’s Hoeffding-type inequality the summation graph-dependent bounded variables. These extend McDiarmid’s difference to cases.

In this paper we prove that the wrapped Butterry graph WBF(d;n) of degree d and dimension n is decomposable into Hamilton cycles. This answers a conjecture of D. Barth and A. Raspaud who solved the case d = 2.

ARTICLE INFO An H-magic labeling in a H-decomposable graph G is a bijection f : V (G) ∪ E(G) → {1, 2, ..., p+ q} such that for every copy H in the decomposition, ∑

Abstract: Decomposable graphs are known for their tedious and complicated Markov update steps. Instead of modelling them directly, this work introduces a class of tree-dependent bipartite graphs that span the projective space of decomposable graphs. This is achieved through dimensionality expansion that causes the graph nodes to be conditionally independent given a latent tree. The Markov updat...

We show in this paper that the circulant graph G( 2”‘, 4) is Hamiltonian decomposable, and propose a recursive construction method. This is a partial answer to a problem posed by B. Alspach. @ 1997 Published by Elsevier Science B.V.

The motivation for this paper is the integer linear programming approach to learning the structure of a decomposable graphical model. We have chosen to represent decomposable models by means of special zero-one vectors, named characteristic imsets. Our approach leads to the study of a special polytope, defined as the convex hull of all characteristic imsets for chordal graphs, named the chordal...

We derive normal approximation bounds in the Wasserstein distance for sums of generalized U-statistics, based on a general bound functionals independent random variables arbitrary distributions. Those are applied to combined weights subgraphs Erdős–Rényi graph, extending graph counting results Barbour et al. (A central limit theorem decomposable with applications graphs, J. Combin. Theory Ser. ...

Applications of graph and hypergraph decomposition techniques to SAT solving have been studied under various conditions. Theoretical research focused on the direction given by tree decompositions, while practical approaches either integrated tree decomposition guidance into existing SAT solver, or studied splitting techniques using hypergraph cuts. In this article we present a uniform and gener...