A graph G is well-covered provided each maximal independent set of vertices has the same cardinality. The term sk of the independence sequence (s0, s1, . . . , sα) equals the number of independent k-sets of vertices of G. We investigate constraints on the linear orderings of the terms of the independence sequence of well-covered graphs. In particular, we provide a counterexample to the recent u...

A graph is well covered if every maximal independent set has the same size and very well covered if every maximal independent set contains exactly half the number of vertices. In this paper, we present an alternative characterization of a certain sub-class of well-covered graphs and show that this generalizes a characterization of very well covered graphs given by Favaron 3].

Remarkable breakthroughs have been made recently in obtaining approximate solutions to some fundamental NP-hard problems, namely Max-Cut, Max k-Cut, Max-Sat, Max-Dicut, Max-bisection, k-vertex coloring, maximum independent set, etc. All these breakthroughs involve polynomial time randomized algorithms based upon semidefinite programming, a technique pioneered by Goemans and Williamson. In this ...

Acknowledgements Gracias a la cigueña y quienes, no siendo su decisión, han tenido que vivir en mi tiempo y beber junto a mí y junto a Baco. Gracias por ser mis contemporáneos, y que la casualidad nos haya llevado a conocernos y tal vez, ver un poco más que un autómata el uno en el otro. Gracias a mi asesor Mauricio Velasco a quien ha dedicado gran parte de su tiempo a guíar este proyecto, a mi...