On the infinity of the set of boundary classes for the edge 3-colorability problem

Abstract

Abstract —The set of boundary classes for the edge 3-colorability problem is proved to be infinite. DOI: 10.1134/S1990478910020109Key words: boundary class, edge 3 -colorability problem INTRODUCTIONA series of articles [1–4] studies the boundary between the “simple” and “complex” classes of graphsas regards various problems concerning graphs in the family of hereditary classes of graphs , whichare the classes closed under isomorphisms and vertex deletion. Every hereditary class Xof graphs canbe defined by a set of its forbidden induced subgraphs S , and the usual notation is X= Free( S ).If S isfinite then the class Xis called finitely defined .In all articles of the series, the study of the boundary rests on the concepts of simple, complex, andboundary classes of graphs for the problem under consideration. A hereditary class of graphs is calledΠ -simple whenever the problem Π in this class is polynomially solvable, and otherwise it is calledΠ -hard . A hereditary class X of graphs is called Π