On the cycle polytope of a directed graph and its relaxations
✍ Scribed by Egon Balas; Rüdiger Stephan
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 166 KB
- Volume
- 54
- Category
- Article
- ISSN
- 0028-3045
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
We provide upper estimates on the spectral radius of a directed graph. In particular w e prove that the spectral radius is bounded by the maximum of the geometric mean of in-degree and out-degree taken over all vertices.
## Abstract In this note, we show how the determinant of the distance matrix __D(G__) of a weighted, directed graph __G__ can be explicitly expressed in terms of the corresponding determinants for the (strong) blocks __G~i~__ of __G__. In particular, when cof __D(G__), the sum of the cofactors of _
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