Abstract
In this article, we deal with graphs modelling interconnection networks of parallel systems (parallel computers, networks of workstations, etc.). We want to share the nodes of such a network between many users, each one needing a given number of nodes. Thus, a graph G with N vertices is said to be decomposable if for each set { n 1,…, n k } whose sum is equal to N, there exists a partition V 1,…, V k of V( G) such that for each i, 1⩽ i⩽ k, | V i |= n i and the subgraph induced by V i is connected. We show that determining whether a given tripode (three disjoint chains connected by one extremity to a same new vertex) is decomposable can be done by a polynomial algorithm.
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