Two relations for median graphs

AbstractWe generalize the well-known relation for trees n−m=1 to the class of median graphs in the following way. Denote by qi the number of subgraphs isomorphic to the hypercube Qi in a median graph. Then, ∑i⩾0(−1)iqi=1. We also give an explicit formula for the number of Θ-classes in a median graph as k=−∑i⩾0(−1)iiqi

Recognizing Partial Cubes in Quadratic Time

We show how to test whether a graph with n vertices and m edges is a partial cube, and if so how to find a distance-preserving embedding of the graph into a hypercube, in the near-optimal time bound O(n^2), improving previous O(nm)-time solutions.Comment: 25 pages, five figures. This version significantly expands previous versions, including a new report on an implementation of the algorithm and experiments with i

Query-based extracting: how to support the answer?

Human-made query-based summaries commonly contain information not explicitly asked for. They answer the user query, but also provide supporting information. In order to find this information in the source text, a graph is used to model the strength and type of relations between sentences of the query and document cluster, based on various features. The resulting extracts rank second in overall readability in the DUC 2006 evaluation. Employment of better question answering methods is the key to improve also content-based evaluation results

Groups acting on quasi-median graphs. An introduction

Quasi-median graphs have been introduced by Mulder in 1980 as a generalisation of median graphs, known in geometric group theory to naturally coincide with the class of CAT(0) cube complexes. In his PhD thesis, the author showed that quasi-median graphs may be useful to study groups as well. In the present paper, we propose a gentle introduction to the theory of groups acting on quasi-median graphs.Comment: 16 pages. Comments are welcom