Collective Tree 1-Spanners for Interval Graphs

Abstract. In this paper we study the existence of a small set T of spanning trees that collectively “1-span” an interval graph G. In particular, for any pair of vertices u, v we require a tree T ∈ T such that the distance between u and v in T is at most one more than their distance in G. We show that: – there is no constant size set of collective tree 1-spanners for interval graphs (even unit interval graphs), – interval graph G has a set of collective tree 1-spanners of size O(log D), where D is the diameter of G, – interval graphs have a 1-spanner with fewer than 2n − 2 edges. Furthermore, at the end of the paper we state other results on collective tree c-spanners for c > 1 and other more general graph classes.

• Type: Conference
• Year: 2005
• Where: WG
• Authors: Derek G. Corneil, Feodor F. Dragan, Ekkehard Köhler, Chenyu Yan
• Keywords: Collective Tree 1-spanners, Computer Science, Interval Graph G, Interval Graphs, WG 2005