Bi-induced sub graphs and stability number

We define a 2-parametric hierarchy CLAP (m, n) of bi-hereditary classes of graphs, and show that a maximum stable set can be found in polynomial time within each class CLAP (m, n). The classes can be recognized in polynomial time

Clones with finitely many relative R-classes

For each clone C on a set A there is an associated equivalence relation analogous to Green's R-relation, which relates two operations on A iff each one is a substitution instance of the other using operations from C. We study the clones for which there are only finitely many relative R-classes.Comment: 41 pages; proofs improved, examples adde

Contributions to the theory of graphic sequences

AbstractIn this article we present a new version of the Erdős-Gallai theorem concerning graphicness of the degree sequences. The best conditions of all known on the reduction of the number of Erdős-Gallai inequalities are given. Moreover, we prove a criterion of the bipartite graphicness and give a sufficient condition for a sequence to be graphic which does not require checking of any Erdős-Gallai inequality