Disjoint Cycles in Directed Graphs on the Torus and the Klein Bottle

Guoli Ding; A. Schrijver; P. D. Seymour

doi:10.1006/jctb.1993.1029

Disjoint Cycles in Directed Graphs on the Torus and the Klein Bottle

Guoli Ding
, A. Schrijver
, P. D. Seymour

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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 P. D. Seymour. This paper gives a shorter proof of that result.

Original language	English (US)
Pages (from-to)	40-45
Number of pages	6
Journal	Journal of Combinatorial Theory, Series B
Volume	58
Issue number	1
DOIs	https://doi.org/10.1006/jctb.1993.1029
State	Published - May 1993
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1006/jctb.1993.1029

Cite this

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abstract = "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 P. D. Seymour. This paper gives a shorter proof of that result.",

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N2 - 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 P. D. Seymour. This paper gives a shorter proof of that result.

AB - 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 P. D. Seymour. This paper gives a shorter proof of that result.

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Disjoint Cycles in Directed Graphs on the Torus and the Klein Bottle

Abstract

All Science Journal Classification (ASJC) codes

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