The Connectivities of Leaf Graphs of Sets of Points in the Plane

KANEKO, Atsushi; YOSHIMOTO, Kiyoshi

Tokyo J. of Math., Tome 24 (2001) no. 2, p. 559-566 / Harvested from Project Euclid

Résumé

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.

Publié le : 2001-12-15
Classification:

@article{1255958194,
     author = {KANEKO, Atsushi and YOSHIMOTO, Kiyoshi},
     title = {The Connectivities of Leaf Graphs of Sets of Points in the Plane},
     journal = {Tokyo J. of Math.},
     volume = {24},
     number = {2},
     year = {2001},
     pages = { 559-566},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1255958194}
}

KANEKO, Atsushi; YOSHIMOTO, Kiyoshi. The Connectivities of Leaf Graphs of Sets of Points in the Plane. Tokyo J. of Math., Tome 24 (2001) no. 2, pp.  559-566. http://gdmltest.u-ga.fr/item/1255958194/