Boundary classes of graphs for some recognition problems

The class of all graphs in which every connected component is a tree with at most three leaves and the class of line graphs of this class are considered in the article. There is a series of well-known problems for which these classes are boundary classes. We study common properties of such problems. Namely, we prove a sufficient condition for the considered classes to be boundary classes. Using the obtained tool we add 8 new cases of given classes being boundary classes to known ones. Bibl. 10.