In the context on the UNL project, we focus on the automatization of enconversion process, that is the building of UNL graphs from sentences. We present an extension of the UNL graph structure aiming at handling lexical and relational ambiguities. On this intermediate structure, we can apply ant algorithm propagation of conceptual vectors and other constraints. Graph nodes and relations have a ...

The reconstruction conjecture claims that every graph on at least three vertices is uniquely determined by its collection of vertex deleted subgraphs. Even though it is one of the foremost unsolved problems in Graph Theory, work on it has slowed down, may be due to the general feeling that existing techniques are not likely to lead to a complete solution. Here we give the results that have appe...

In the context on the UNL project, we focus on the automatization of enconversion process, that is the building of UNL graphs from sentences. We present an extension of the UNL graph structure aiming at handling lexical and relational ambiguities. On this intermediate structure, we can apply ant algorithm propagation of conceptual vectors and other constraints. Graph nodes and relations have a ...

We consider the problem of updating a directed minimum cost spanning tree (DMST), when edges are deleted from or inserted to a weighted directed graph. This problem apart from being a classic for directed graphs, is to the best of our knowledge a wide open aspect for the field of dynamic graph algorithms. Our contributions include results on the hardness of updates, a dynamic algorithm for upda...

The reconstruction conjecture states that the multiset of vertex-deleted subgraphs of a graph determines the graph, provided it has at least 3 vertices. This problem was independently introduced by Stanis law Ulam (1960) and Paul Kelly (1957). In this paper, we prove the conjecture by elementary methods. It is only necessary to integrate the Lenkle potential of the Broglington manifold over the...

A regular nonempty graph Γ is called edge regular, whenever there exists a nonegative integer λΓ, such that any two adjacent vertices of Γ have precisely λΓ common neighbours. An edge regular graph Γ with at least one pair of vertices at distance 2 is called amply regular, whenever there exists a nonegative integer μΓ, such that any two vertices at distance 2 have precisely μΓ common neighbours...

In this work we present our approach to (simple di-)graph transformation based on an algebra of boolean matrices. Rules are represented as boolean matrices for nodes and edges and derivations can be efficiently characterized with boolean operations only. Our objective is to analyze properties inherent to rules themselves (without considering an initial graph), so this information can be calcula...

A graph G is said to be hypohamiltonian if G is not hamiltonian but for each v ∈ V (G) the vertex deleted subgraph G − v is hamiltonian. In this paper we show that there is no hypohamiltonian graph on 17 vertices and thereby complete the answer to the question, “for which values of n do there exist hypohamiltonian graphs on n vertices?”. In addition we present an exhaustive list of hypohamilton...

An edge-deleted subgraph of a graph G is an edge-card. A decard consists of an edge-card and the degree of the missing edge. The degree-associated edge-reconstruction number of a graph G, denoted dern(G), is the minimum number of decards that suffice to reconstruct G. The adversary degree-associated edge-reconstruction number adern(G) is the least k such that every set of k decards determines G...

Vertex deletion is a well known NP-complete problem. An empirical method for estimating the number of vertices that need to be deleted to make a graph bipartite is presented. The estimator has been developed by modelling the problem using random graphs where an edge is present with a xed probability p. The method works in O(n 2) time, where n is the number of vertices in the graph. The estimato...