Representing triangulated graphs in stars

A graphG is calledrepresentable in a tree T, ifG is isomorphic to the intersection graph of a family of subtrees ofT. In this paper those graphs are characterized which are representable in some subdivision of theK1,n. In the finite case polynomial-time recognition algorithms of these graphs are given. But this concept can be generalized to essentially infinite graphs by using no more trees but ‘tree-like’ posets and representability of graphs in these posets.