‎A tree containing exactly two non-pendant vertices is called a double-star‎. ‎Let $k_1$ and $k_2$ be two positive integers‎. ‎The double-star with degree sequence $(k_1+1‎, ‎k_2+1‎, ‎1‎, ‎ldots‎, ‎1)$ is denoted by $S_{k_1‎, ‎k_2}$‎. ‎It is known that a cubic graph has an $S_{1,1}$-decomposition if and only if it contains a perfect matching‎. ‎In this paper‎, ‎we study the $S_{1,2}$-decomposit...

the star-mesh transformation allows the reduction of nodes in an electrical circuit. the gauss elimination method allows the reduction of unknowns in a system of linear equations . triangular decomposition can be used to find the inverse of a matrix. in this paper the coherence between these methods are discussed. it is shown that the gauss elimination method gives the same formula for star-mes...

We introduce the notion of compatible star decompositions of simple polygons. In general, given two polygons with a correspondence between their vertices, two polygonal decompositions of the two polygons are said to be compatible if there exists a one-to-one mapping between them such that the corresponding pieces are defined by corresponding vertices. For compatible star decompositions, we also...

In this paper we show how a theorem in plane geometry can be converted into an O(n log n) algorithm for decomposing a polygon into star-shaped subsets. The computational efficiency or this new decomposition contrasts with the heavy computational burden of existing methods. 1.0 Introduction The decomposition of a simple planar polygon into simpler components plays an important role in syntactic ...

In this paper we consider the class of simple graphs defined by excluding, as inducedsubgraphs, even holes (i.e. chordless cycles of even length). These graphs are known aseven-hole-free graphs. We prove a decomposition theorem for even-hole-free graphs, thatuses star cutsets and 2-joins. This is a significant strengthening of the only other pre-viously known decomposition of ev...

This paper proposes an effective framework to compute the visibility guarding and star decomposition of 3D solid shapes. We propose a progressive integer linear programming algorithm to solve the guarding points that can visibility cover the entire shape; we also develop a constrained region growing scheme seeded on these guarding points to get the star decomposition. We demonstrate this guardi...

In this paper, a new general decomposition theory inspired from modular graph decomposition is presented. Our main result shows that, within this general theory, most of the nice algorithmic tools developed for modular decomposition are still efficient. This theory not only unifies the usual modular decomposition generalisations such as modular decomposition of directed graphs or decomposition ...

Star graphs are Cayley graphs of symmetric groups of permutations, with transpositions as the generating sets. A star graph is a preferred interconnection network topology to a hypercube for its ability to connect a greater number of nodes with lower degree. However, an attractive property of the hypercube is that it has a Hamiltonian decomposition, i.e. its edges can be partitioned into disjoi...