On Partitioning the Edges of Graphs into Connected Subgraphs

J√ľnger, Michael and Reinelt, Gerhard and Pulleyblank, William R. (1985) On Partitioning the Edges of Graphs into Connected Subgraphs.
Published in: Journal of Graph Theory Vol. 9 (4). pp. 539-549.

Abstract

For any positive integer s, an s-partition of a graph G = (V, E) is a partition of E into E1 E2 Ek, where Ei = s for 1 i k - 1 and 1 Ek s and each Ei induces a connected subgraph of G. We prove (i) If G is connected, then there exists a 2-partition, but not necessarily a 3-partition; (ii) If G is 2-edge connected, then there exists a 3-partition, but not necessarily a 4-partition; (iii) If G is 3-edge connected, then there exists a 4-partition; (iv) If G is 4-edge connected, then there exists an s-partition for all s.


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Date Deposited: 31 Aug 2010 14:50
Last Modified: 04 Jul 2014 09:34
URI: http://e-archive.informatik.uni-koeln.de/id/eprint/817