Deformations of dotted graphs consisting of standard circles

Abstract

Dotted graphs are certain finite graphs with vertices of degree 2 called dots in the $xy$-plane $\mathbb{R}^2$, and a dotted graph is said to be admissible if it is associated with a lattice polytope in $\mathbb{R}^2$ each of whose edge is parallel to the $x$-axis or the $y$-axis. A dotted graph is said to be reducible if certain types of deformations are applicable. In this paper, we investigate the reducibility of admissible dotted graphs in certain simple forms consisting of standard circles.