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Disk/band surfaces of spatial graphs. (English) Zbl 0891.05021
Suppose that $$\Gamma$$ is an embedding of a graph $$G$$ into $$\mathbb{R}^3$$. A disk/band surface $$S$$ of $$\Gamma(G)$$ is a compact, orientable surface in $$\mathbb{R}^3$$ such that $$\Gamma(G)$$ is the deformation retract of $$S$$ contained in the interior of $$S$$. If $$G$$ is a connected planar graph with embedding $$\Gamma$$, then there is a disk/band surface of $$\Gamma(G)$$ satisfying a certain linking condition. From this theorem follows the result that the linking numbers of disjoint pairs in the set of boundary/outermost cycles with respect to a fixed planar embedding determine the homology class of $$\Gamma(G)$$.
Reviewer: M.Marx (Pensacola)

##### MSC:
 05C10 Planar graphs; geometric and topological aspects of graph theory
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