We tackle the problem of representing association rules for a prediction purpose. We approach this problem by introducing a novel data structure for representing association rules (now seen as classification/regression rules). Unseen cases are fitted into a graph like structure that avoids any type of sorting procedure. The graph indexes the items present in the rules so that only rules with th...

Given a graph G = (V; E) and a real weight for each vertex of G, the vertex-weight of a matching is deened to be the sum of the weights of the vertices covered by the matching. In this paper we present a linear time algorithm for nding a maximum vertex-weighted matching in a strongly chordal graph, given a strong elimination ordering. The algorithm can be specialized to nd a maximum cardinality...

If G is a bridgeless cubic graph, Fulkerson conjectured that we can find 6 perfect matchings M1, . . . ,M6 of G with the property that every edge of G is contained in exactly two of them and Berge conjectured that its edge set can be covered by 5 perfect matchings. We define τ(G) as the least number of perfect matchings allowing to cover the edge set of a bridgeless cubic graph and we study thi...

We consider graph properties that can be checked from labels, i.e., bit sequences, of logarithmic length attached to vertices. We prove that there exists such a labeling for checking a first-order formula with free set variables in the graphs of every class that is nicely locally clique-width-decomposable. This notion generalizes that of a nicely locally tree-decomposable class. The graphs of s...

A new, constructive proof with a small explicit constant is given to the Erdős-Pyber theorem which says that the edges of a graph on n vertices can be partitioned into complete bipartite subgraphs so that every vertex is covered at most O(n/ logn) times. The theorem is generalized to uniform hypergraphs. Similar bounds with smaller constant value is provided for fractional partitioning both for...

For a brick apart from a few small graphs, Lovász (1987) proposed a conjecture on the existence of an edge whose deletion results in a graph with only one brick in its tight cut decomposition. Carvalho, Lucchesi, and Murty (2002) confirmed this conjecture by showing the existence of such two edges. This paper generalizes the result obtained by Carvalho et al. to the case of irreducible near-bri...

A new, constructive proof with a small explicit constant is given to the Erdős-Pyber theorem which says that the edges of a graph on n vertices can be partitioned into complete bipartite subgraphs so that every vertex is covered at most O(n/ log n) times. The theorem is generalized to uniform hypergraphs. Similar bounds with smaller constant value is provided for fractional partitioning both fo...

A maximum stable set in a graph G is a stable set of maximum cardinality. S is called a local maximum stable set of G, and we write S ∈ Ψ(G), if S is a maximum stable set of the subgraph induced by the closed neighborhood of S. A greedoid (V,F) is called a local maximum stable set greedoid if there exists a graph G = (V,E) such that F = Ψ(G). Nemhauser and Trotter Jr. [27], proved that any S ∈ ...

Let G be a matching-covered graph, i.e., every edge is contained in a perfect matching. An edge subsetX ofG is feasible if there exists two perfect matchingsM1 andM2 such that |M1∩X| 6≡ |M2∩X| (mod 2). Lukot’ka and Rollová proved that an edge subset X of a regular bipartite graph is not feasible if and only if X is switching-equivalent to ∅, and they further ask whether a non-feasible set of a ...