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June 1997 Disk/Band Surfaces of Spatial Graphs
Teruhiko SOMA, Hideyuki SUGAI, Akira YASUHARA
Tokyo J. Math. 20(1): 1-11 (June 1997). DOI: 10.3836/tjm/1270042393

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 $G$.

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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

Information

Published: June 1997
First available in Project Euclid: 31 March 2010

zbMATH: 0891.05021
MathSciNet: MR1451853
Digital Object Identifier: 10.3836/tjm/1270042393

Rights: Copyright © 1997 Publication Committee for the Tokyo Journal of Mathematics

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Vol.20 • No. 1 • June 1997
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