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Diameter and Treewidth in Minor-Closed Graph Families, Revisited

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Abstract

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.

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Authors and Affiliations

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

    Erik D. Demaine & Mohammad Taghi Hajiaghayi

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  1. Erik D. Demaine
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  2. Mohammad Taghi Hajiaghayi
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Correspondence to Erik D. Demaine or Mohammad Taghi Hajiaghayi.

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Demaine, E., Hajiaghayi, M. Diameter and Treewidth in Minor-Closed Graph Families, Revisited. Algorithmica 40, 211–215 (2004). https://doi.org/10.1007/s00453-004-1106-1

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  • DOI: https://doi.org/10.1007/s00453-004-1106-1

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