Χαρακτηρισμός νέων κλάσεων τέλειων γραφημάτων και αγλόριθμοι χρωματισμού και μέγιστων διαδρομών

Abstract

In this work we provide characterizations of two new classes of perfect graphs, namely colinear and linear graphs. Moreover, we present polynomial-time algorithms or NP-completeness results for various types of the coloring problem on graphs and polynomial-time algorithms for the longest path problem on perfect graphs. In particular, motivated by the de nition of linear coloring on simplicial complexes, recently introduced in the context of algebraic topology, we introduce the colinear coloring on graphs, and propose a polynomial algorithm for colinearly coloring any graph G. Based on the colinear coloring, we de ne the