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On optimal orientations of cartesian products of graphs (I)

✍ Scribed by K.M. Koh; E.G. Tay


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
807 KB
Volume
190
Category
Article
ISSN
0012-365X

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πŸ“œ SIMILAR VOLUMES


On optimal orientations of Cartesian pro
✍ Koh, K. M.; Tay, E. G. πŸ“‚ Article πŸ“… 1998 πŸ› John Wiley and Sons 🌐 English βš– 220 KB

For a graph G, let D(G) be the family of strong orientations of G. Define d ៝ (G) Γ… min {d(D)Γ‰D √ D(G)} and r(G) Γ… d ៝ (G) 0 d(G), where d(D) [respectively, d(G)] denotes the diameter of the digraph D (respectively, graph G). Let G 1 H denote the Cartesian product of the graphs G and H, and C p , th

On optimal orientations of Cartesian pro
✍ Koh, K. M.; Tay, E. G. πŸ“‚ Article πŸ“… 1997 πŸ› John Wiley and Sons 🌐 English βš– 122 KB

For a graph G , let D ( G ) be the family of strong orientations of G , and define d ៝ ( G ) Γ… min{d(D)Γ‰D √ D(G)}, where d(D) is the diameter of the digraph D. In this paper, we evaluate the values of d ៝ (C 2n 1

Counting stable sets on Cartesian produc
✍ Florence Forbes; Bernard Ycart πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 552 KB

We study the generating functions for the number of stable sets of all cardinalities, in the case of graphs which are Cartesian products by paths, cycles, or trees. Explicit results are given for products by cliques. Algorithms based on matrix products are derived for grids, cylinders, toruses and h

A theorem on integer flows on cartesian
✍ Wilfried Imrich; Riste Ε krekovski πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 72 KB

## Abstract It is shown that the Cartesian product of two nontrivial connected graphs admits a nowhere‐zero 4‐flow. If both factors are bipartite, then the product admits a nowhere‐zero 3‐flow. Β© 2003 Wiley Periodicals, Inc. J Graph Theory 43: 93–98, 2003

Embedding Cartesian Products of Graphs i
✍ Thomas Andreae; Michael NΓΆlle; Gerald Schreiber πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 172 KB

## Given a Cartesian product G of nontrivial connected graphs G i and the n-dimensional base B de Bruijn graph D = D B (n), it is investigated whether or not G is a spanning subgraph of D. Special attention is given to graphs G 1 Γ— β€’ β€’ β€’ Γ— G m which are relevant for parallel computing, namely, to