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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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