From kernels in directed graphs to fixed points and negative cycles in Boolean networks

Authors:
Adrien Richard;Paul Ruet
Affiliations:
Laboratoire I3S, UMR 6070 CNRS & Universitéé de Nice-Sophia Antipolis, 2000 route des Lucioles, 06903 Sophia Antipolis, France;CNRS, Laboratoire Preuves, Programmes et Systèmes, Université Paris Diderot - Paris 7, Case 7014, 75205 Paris Cedex 13, France
Venue:
Discrete Applied Mathematics
Year:
2013

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Abstract

We consider a class of Boolean networks called and-nets, and we address the question of whether the absence of negative cycle in local interaction graphs implies the existence of a fixed point. By defining correspondences with the notion of kernel in directed graphs, we prove a particular case of this question, and at the same time, we prove new theorems in kernel theory, on the existence and unicity of kernels.