A p-star is a complete bipartite graph K1,p with one center node and p leaf nodes. In this paper we propose the first distributed self-stabilizing algorithm for graph decomposition into p-stars. For a graph G and an integer p ≥ 1, this decomposition provides disjoint components of G where each component forms a p-star. We prove convergence and correctness of the algorithm under an unfair distri...

The Macro-star graph which has the star graph as a basic module has node symmetry, maximum fault tolerance, and hierarchical decomposition property. And, it is an interconnection network which improves a network cost against the star graph. A Matrix-star graph also has such a good properties of the Macro-star graph and is an interconnection network which has a lower network cost than the Macro-

This paper is a continuation of the first two parts of this series ([I],[II]). It relies on the formulation of the Kepler conjecture in [F]. The terminology and notation of this paper are consistent with these earlier papers, and we refer to results from them by prefixing the relevant section numbers with I, II, or F. Around each vertex is a modification of the Voronoi cell, called the V -cell ...

This paper is a continuation of the first two parts of this series ([I],[II]). It relies on the formulation of the Kepler conjecture in [F]. The terminology and notation of this paper are consistent with these earlier papers, and we refer to results from them by prefixing the relevant section numbers with I, II, or F. Around each vertex is a modification of the Voronoi cell, called the V -cell ...

We prove a decomposition theorem for even-hole-free graphs. The decompositions used are 2-joins and star, double-star and triple-star cutsets. This theorem is used in the second part of this paper to obtain a polytime recognition algorithm for even-hole-free graphs.

Simplification or decomposition is a common strategy to handle large geometric models, which otherwise require excessive computation to process. Star-shaped decomposition partitions a model into a set of star-shaped components. A model is star shaped if and only if there exists at least one point which can see all the points of the model. Due to this interesting property, decomposing a model in...

Automatic classification of stellar spectra is an important research component astronomical data processing and the basis for studying evolution parameter measurements. As a rare kind spectra, carbon star put forward more efficient accurate requirements methods. The traditional manual methods have disadvantages slow speed low accuracy, which can no longer meet practical needs automatic massive ...

The Ascending Subgraph Decomposition (ASD) Conjecture asserts that every graph G with ( n+1 2 ) edges admits an edge decomposition G = H1 ⊕ · · · ⊕ Hn such that Hi has i edges and it is isomorphic to a subgraph of Hi+1, i = 1, . . . , n − 1. We show that every bipartite graph G with ( n+1 2 ) edges such that the degree sequence d1, . . . , dk of one of the stable sets satisfies di ≥ n − i + 1, ...