We give an alternative characterization for well-covered graphs and restrict this to a characterization for very well covered graphs. We state the conditions under which the intersection of a pair of maximal independent sets of a well-covered graph is maximal and use this result to deene and characterize two recursively decomposable sub-classes of well-covered graphs, one properly containing th...

This paper introduces the ulmods, a generalisation of modules for the homogeneous relations. We first present some properties of the ulmod family, then show that, if the homogeneous relation fulfills some natural axioms, the ulmod family has a unique decomposition tree. Under a certain size assumption we show that this tree can be computed in polynomial time. We apply this theory to a new tourn...

In this paper, we introduce a subclass of chordal graphs which contains $d$-trees and show that their complement are vertex decomposable and so is shellable and sequentially Cohen-Macaulay.

This paper introduces the ulmods, a generalisation of modules for the homogeneous relations. We first present some properties of the ulmod family, then show that, if the homogeneous relation fulfills some natural axioms, the ulmod family has a unique decomposition tree. Under a certain size assumption we show that this tree can be computed in polynomial time. We apply this theory to a new tourn...

A cycle in a multipartite graph G is gregarious if it contains at most one vertex from each partite set of G. The complete n-partite graph with partite sets of size m, denoted by Kn(m) is shown to have a decomposition into gregarious 4-cycles. The notion of a gregarious 4-cycle decomposition of this type was introduced in [3]. A 4-cycle decomposition of Kn(m) is circular if it is it is invarian...

A graph G is arbitrarily decomposable into closed trails (ADCT) if the following is true: Whenever (l1, . . . , lp) is a sequence of integers adding up to |E(G)| and there is a closed trail of length li in G for i = 1, . . . , p, then there is a sequence (T1, . . . , Tp) of pairwise edge-disjoint closed trails in G such that Ti is of length li for i = 1, . . . , p. In the paper it is proved tha...

We present a construction of constant weight codes based on the unique decomposition of elements in lattices. The conditions for unique primary decomposition and unique irreducible decomposition in lattices are discussed and the connections with decomposition of ideals in Noetherian commutative rings established. The source alphabet in our proposed construction is a set of uniquely decomposable...

In NTCIR-10, we participated in the subtask of Subtopic Mining. We classify test topics into two types: role-explicit topic and roleimplicit topic. According to the topic type, we devise different approaches to perform subtopic mining. Specifically, for roleexplicit topics, we propose an approach of modifier graph based subtopic mining. The key idea is that: The modifier graph corresponding to ...

The requirements for a main memory data storage model are both compactness and efficient processing for all database operations. The DBGraph storage model, proposed in this paper, achieves these goals. By representing the entire database in a unique graph-based data structure, called DBGraph, it fully exploits the directaccess capability of main memory systems. For example, Selection, Join and ...

A graph is locally irregular if every two adjacent vertices have distinct degrees. Recently, Baudon et al. introduced the notion of decomposition into locally irregular subgraphs. They conjectured that for almost every graphG, there exists a minimum integer χirr(G) such thatG admits an edge-partition into χ ′ irr(G) classes, each of which induces a locally irregular graph. In particular, they c...