Translator Disclaimer
December 2001 The Connectivities of Leaf Graphs of Sets of Points in the Plane
Atsushi KANEKO, Kiyoshi YOSHIMOTO
Tokyo J. Math. 24(2): 559-566 (December 2001). DOI: 10.3836/tjm/1255958194

Abstract

Let $U$ be a finite set of points in general position in the plane. We consider the following graph $\mathcal{G}$ determined by $U$. A vertex of $\mathcal{G}$ is a spanning tree of $U$ whose edges are straight line segments and do not cross. Two such trees $\mathbf{t}$ and $\mathbf{t}'$ are adjacent if for some vertex $u\in U$, $\mathbf{t}-u$ is connected and coincides with $\mathbf{t}'-u$. We show that $\mathcal{G}$ is 2-connected, which is the best possible result.

Citation

Download Citation

Atsushi KANEKO. Kiyoshi YOSHIMOTO. "The Connectivities of Leaf Graphs of Sets of Points in the Plane." Tokyo J. Math. 24 (2) 559 - 566, December 2001. https://doi.org/10.3836/tjm/1255958194

Information

Published: December 2001
First available in Project Euclid: 19 October 2009

zbMATH: 0996.05085
MathSciNet: MR1874990
Digital Object Identifier: 10.3836/tjm/1255958194

Rights: Copyright © 2001 Publication Committee for the Tokyo Journal of Mathematics

JOURNAL ARTICLE
8 PAGES


SHARE
Vol.24 • No. 2 • December 2001
Back to Top