Su, X.-Y., A result on decompositions of regular graphs, Discrete Mathematics 105 (1992) 323-326. We prove that for any connected graph G and any integer r which is a common multiple of the degrees of the vertices in G, there exists a connected, r-regular, and G-decomposable graph H such that x(H) = x(G) and o(H) = w(G), where x and w are the chromatic number and the clique number, respectively...

Logical analysis of data (LAD) is one of the methodologies for extracting knowledge as a Boolean function f from a given pair of data sets (T; F ) on attributes set S of size n, in which T (resp., F ) f0; 1g n denotes a set of positive (resp., negative) examples for the phenomenon under consideration. In this paper, we consider the case in which extracted knowledge has a decomposable structure;...

In this paper we introduce the class of strongly decomposable discrete sets and give an efficient algorithm for reconstructing discrete sets of this class from four projections. It is also shown that every Q-convex set (along the set of directions {x, y}) consisting of several components is strongly decomposable. As a consequence of strong decomposability we get that in a subclass of hv-convex ...

‎Recently‎, ‎some techniques such as adding whiskers and attaching graphs to vertices of a given graph‎, ‎have been proposed for constructing a new vertex decomposable graph‎. ‎In this paper‎, ‎we present a new method for constructing vertex decomposable graphs‎. ‎Then we use this construction to generalize the result due to Cook and Nagel‎.

For a tree T , the graph X is T -decomposable if there exists a partition of the edge set of X into isomorphic copies of T . In 1963, Ringel conjectured that K2m+1 can be decomposed by any tree with m edges. Graham and Häggkvist conjectured more generally that every 2m-regular graph can be decomposed by any tree with m edges. Fink showed in 1994 that for any directed tree T with m arcs, the dir...

A walk on an edge-colored graph G is a path in G which contains each edge at least once, and the trace of a walk w is the sequence of edge-colors seen in w. We investigate the walk realizability problem, which is to decide, given an edge-colored graph G and a string x of colors, if there is a walk on G with trace x. We de ne a method of decomposing graphs into linear chains, and show that the n...

The topological filtration on K ′ 0 of a Severi-Brauer variety is computed if the quotient of its index and exponent is a squarefree number and for each prime p dividing this quotient the p -primary component of the corresponding division algebra is decomposable. This gives in particular a description of Ch for such varieties. Let D be a central simple algebra over a field F and X = SB(D) the S...

Let T be a bounded operator on a complex Banach space X. If V is an open subset of the complex plane, we give a condition sufficient for the mapping f(z) 7→ (T − z)f(z) to have closed range in the Fréchet space H(V, X) of analytic X-valued functions on V . Moreover, we show that there is a largest open set U for which the map f(z) 7→ (T − z)f(z) has closed range in H(V, X) for all V ⊆ U . Final...

We show that, for a pseudo-proper smooth noetherian formal scheme $\mathfrak{X}$ over positive characteristic $p$ field, its truncated De Rham complex up to the is decomposable. Moreover, if dimension of exactly $p$, then full Along way we establish Cartier isomorphism associated morphism schemes.

Let F be a multifunction with values in Lp(Ω, X). In this note, we study which regularity properties of F are preserved when we consider the decomposable hull of F .