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

DOI10.1016/j.dam.2012.10.022zbMath1315.05068OpenAlexW2136852170MaRDI QIDQ1949117

Paul Ruet, Adrien Richard

Publication date: 25 April 2013

Published in: Discrete Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.dam.2012.10.022

zbMATH Keywords

fixed pointdirected graphkerneldiscrete dynamical systemodd cyclenegative cycle

Mathematics Subject Classification ID

Paths and cycles (05C38) Directed graphs (digraphs), tournaments (05C20) Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) (05C60)

Related Items (10)

Fixed points in conjunctive networks and maximal independent sets in graph contractions ⋮ Synchronizing Boolean networks asynchronously ⋮ Positive and negative cycles in Boolean networks ⋮ Local Negative Circuits and Cyclic Attractors in Boolean Networks with at most Five Components ⋮ Negative local feedbacks in Boolean networks ⋮ Fixed points and connections between positive and negative cycles in Boolean networks ⋮ Asynchronous Boolean networks and hereditarily bijective maps ⋮ Local cycles and dynamical properties of Boolean networks ⋮ Isometries of the hypercube: a tool for Boolean regulatory networks analysis ⋮ Fixed point theorems for Boolean networks expressed in terms of forbidden subnetworks

Cites Work

• On kernels and semikernels of digraphs
• Graphic requirements for multistability and attractive cycles in a Boolean dynamical framework
• An extension of a combinatorial fixed point theorem of Shih and Dong
• Negative circuits and sustained oscillations in asynchronous automata networks
• A combinatorial analogue of the Jacobian problem in automata networks
• Discrete dynamical systems
• Local negative circuits and fixed points in non-expansive Boolean networks
• Perfect graphs, kernels, and cores of cooperative games
• Necessary conditions for multistationarity in discrete dynamical systems
• Solutions of irreflexive relations
• Multistationarity, the basis of cell differentiation and memory. I. Structural conditions of multistationarity and other nontrivial behavior
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