Abstract
In this paper, we show that, for any spatial embedding $\Gamma:G\to\mathbf{R}^3$ of a connected planar graph $G$, there exists a disk/band surface of $\Gamma(G)$ satisfying a certain linking condition. As an application of this result, it is proved that the homology class of $\Gamma(G)$ is determined only by the linking numbers of disjoint pairs in the set of boundary/outermost cycles with respect to a fixed planar embedding of $G$.
Citation
Teruhiko SOMA. Hideyuki SUGAI. Akira YASUHARA. "Disk/Band Surfaces of Spatial Graphs." Tokyo J. Math. 20 (1) 1 - 11, June 1997. https://doi.org/10.3836/tjm/1270042393
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