Simple polygons with an infinite sequence of deflations

Thomas Fevens, Antonio Hernandez, Antonio Mesa, Patrick Morin, Michael Soss, Godfried Toussaint

Research output: Contribution to journalArticle

Abstract

Given a simple polygon in the plane, a deflation is defined as the inverse of a flip in the Erdos-Nagy sense. In 1993 Bernd Wegner conjectured that every simple polygon admits only a finite number of deflations. In this note we describe a counterexample to this conjecture by exhibiting a family of polygons on which deflations go on forever.

Original languageEnglish (US)
Pages (from-to)307-311
Number of pages5
JournalBeitrage zur Algebra und Geometrie
Volume42
Issue number2
StatePublished - 2001

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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    Fevens, T., Hernandez, A., Mesa, A., Morin, P., Soss, M., & Toussaint, G. (2001). Simple polygons with an infinite sequence of deflations. Beitrage zur Algebra und Geometrie, 42(2), 307-311.