Journal of Combinatorial Theory, Series B 81, 156162 (2001) NOTE The Separator Theorem for Rooted Directed Vertex Graphs B. S. Panda Department of Computer Science, IPC Unit, BITS Pilani 333 031, India E-mail: bspandabits-pilani.ac.in Received March 24, 2000 In this note we point out a flaw in the separator theorem for rooted directed vertex graphs due to C. L. Monma and V. K. Wei (1986, J. Combin. Theory Ser. B 41, 141181), and present a modified separator theorem for the same class of graphs.  2001 Academic Press 1. INTRODUCTION Let F be a family of non-empty sets. An undirected graph G is an inter- section graph for F if there is a one-to-one correspondence between the ver- tices of G and the sets in F such that two vertices in G are adjacent if and only if the corresponding sets have non-empty intersection. If F is a family of paths in an undirected tree T, then G is called an undirected vertex (UV ) or a path graph. If F is a family of directed paths in a directed tree T, then G is called a directed vertex (DV ) or a directed path graph. Note that a directed tree may have more than one vertex of indegree zero. A rooted directed tree is a directed tree having exactly one vertex of indegree zero. If F is a family of paths in a rooted directed tree T, then G is called a rooted directed vertex (RDV) graph. Monma and Wei [1] presented a unified framework for characterizing UV, DV and RDV graphs. In [1], they presented characterizations of these graphs in terms of clique separator, which are called separator theorems. In this note, we present a counter example to the separator theorem for RDV graphs due to Monma and Wei [1]. We, then, present a modified separator theorem for RDV graphs. doi:10.1006jctb.2000.2001, available online at http:www.idealibrary.com on 156 0095-895601 35.00 Copyright  2001 by Academic Press All rights of reproduction in any form reserved.