This paper concerns the optimal partition of a graph into p connected clusters of vertices, with various constraints on their topology and weight. We consider di erent objectives, depending on the cost of the trees spanning the clusters. This rich family of problems mainly applies to telecommunicati
On the complexity of some edge-partition problems for graphs
β Scribed by Zbigniew Lonc
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 515 KB
- Volume
- 70
- Category
- Article
- ISSN
- 0166-218X
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An extension of the decomposition theorem of Birkhoff-von Neumann theorem is given for the case where entries can be positive or negative. The special case of an integral matrix is discussed and some balancing properties which are trivial for the classical case (non-negative entries only in the matr
For any positive integer s, an s-partition of a graph G = ( ! -( β¬I is a partition of E into El U E2 U U E k, where 14 = s for 1 I i 5 k -1 and 1 5 1 4 1 5 s and each β¬; induces a connected subgraph of G. We prove (i) if G is connected, then there exists a 2-partition, but not neces-(ii) if G is 2-e