Diameter and Treewidth in Minor-Closed Graph Families, Revisited

  title={Diameter and Treewidth in Minor-Closed
Graph Families, Revisited},
  author={E. Demaine and M. Hajiaghayi},
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… Expand
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  • D. Eppstein
  • Mathematics, Computer Science
  • Algorithmica
  • 2000
It is shown that treewidth is bounded by a function of the diameter in a minor-closed family, if and only if some apex graph does not belong to the family, and the O(D) bound above can be extended to bounded-genus graphs. Expand
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