We give necessary and sufficient conditions for a directed graph embedded on the torus or the Klein bottle to contain pairwise disjoint circuits, each of a given orientation and homotopy, and in a given order. For the Klein bottle, the theorem is new. For the torus, the theorem was proved before by
Disjoint circuits on a Klein bottle and a theorem on posets
โ Scribed by Guoli Ding
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 694 KB
- Volume
- 112
- Category
- Article
- ISSN
- 0012-365X
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โฆ Synopsis
Ding, G., Disjoint circuits on a Klein bottle and a theorem on posets, Discrete Mathematics 112 (1993) 81-91.
In this paper, we consider the problem of packing disjoint directed circuits in a digraph drawn on the Klein bottle or on the torus. We formulate a problem on posets which unifies all the problems considered by Ding et al. and by Seymour. Then we generalize all the results of their two papers by proving a theorem on our special posets.
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