In the recent years, several polynomial algorithms of a dynamical nature have been proposed to address the graph isomorphism problem ([GN 02], [SJC 03], etc.). In this paper we propose a generalization of an approach exposed in [GN 02] and find that this dynamical algorithm is covered by a combinatorial approach. It is possible to infer that polynomial dynamical algorithms addressing graph isom...

We provide a family of examples of graph manifolds which admit taut foliations, but no R-covered foliations. We also show that, with very few exceptions, R-covered foliations are taut.

A graph is called matching covered if for its every edge there is a maximum matching containing it. It is shown that minimal matching covered graphs contain a perfect matching.

given a graph $g$, the total dominator coloring problem seeks aproper coloring of $g$ with the additional property that everyvertex in the graph is adjacent to all vertices of a color class. weseek to minimize the number of color classes. we initiate to studythis problem on several classes of graphs, as well as findinggeneral bounds and characterizations. we also compare the totaldominator chro...

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 ∈ ...