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Preprints, Working Papers, ... Year : 2016

Enumerating simple paths from connected induced subgraphs

Abstract

We present an exact formula for the ordinary generating series of the simple paths, also called self-avoiding walks, between any two vertices of a graph. Our formula involves a sum over the connected induced subgraphs and remains valid on weighted and directed graphs. An intermediary result of our approach provides a unifying vision that conciliates several concepts used in the literature for counting simple paths. We obtain a relation linking the Hamiltonian paths and cycles of a graph to its connected dominating sets.
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Dates and versions

hal-01324737 , version 1 (01-06-2016)

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Pierre-Louis Giscard, Paul Rochet. Enumerating simple paths from connected induced subgraphs. 2016. ⟨hal-01324737⟩
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