INTERSECTION GRAPHS OF CONCATENABLE SUBTREES OF GRAPHS

A graph is fraternally oriented if for every three vertices u, v, w th e existence of the edges u --> w and v --> w implies that u and v are adjacent. An acanthus is a graph which is a free tree or is obtained b y adding an edge to a free tree. Two rooted subtrees of an undirected graph are called concatenable if either they are disjoint or their int ersection contains the root of one of them and their union contains no cycle. We prove that a connected graph G is the intersection graph of a family of pairwise concatenable edge subtrees of an undirected grap h if and only if it is the intersection graph of a family of pairwise concatenable edge subtrees of an acanthus if and only if G has a frate rnal orientation such that for every vertex v the subgraphs G(GAMMA(in ) v) and G(GAMMA(out) v) have no directed cycles.