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

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.
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Adrien Richard, Paul Ruet. From kernels in directed graphs to fixed points and negative cycles in Boolean networks. Discrete Applied Mathematics, Elsevier, 2013, 161 (7-8), pp.1106-1117. ⟨10.1016/j.dam.2012.10.022⟩. ⟨hal-01298841⟩

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