, Volume 40, Issue 3, pp 211–215

Diameter and Treewidth in Minor-Closed Graph Families, Revisited


DOI: 10.1007/s00453-004-1106-1

Cite this article as:
Demaine, E. & Hajiaghayi, M. Algorithmica (2004) 40: 211. doi:10.1007/s00453-004-1106-1


Eppstein [5] characterized the minor-closed graph families for which the treewidth is bounded by a function of the diameter, which includes, e.g., planar graphs. This characterization has been used as the basis for several (approximation) algorithms on such graphs (e.g., [2] and [5]–[8]). The proof of Eppstein is complicated. In this short paper we obtain the same characterization with a simple proof. In addition, the relation between treewidth and diameter is slightly better and explicit.

Apex graphs Graph minors Bounded local treewidth Graph algorithms Approximation algorithms 

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.MIT Computer Science and Artificial Intelligence Laboratory, 32 Vassar Street, Cambridge, MA 02139USA

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