TIGHTNESS OF GRAPHS: REALISATIONS WITH THE TWO-PIECE-PROPERTY

摘要

Mappings from graphs into Euclidean space with the two-piece-property are studied. In particular, conditions are given under which a graph admits such a two-piece-property mapping, immersion or embedding. A typical condition is the 3-connectivity or 4-connectivity. The maximum codimension is closely related to the invariant κ defined by van der Hoist, Laurent and Schrijver.