A Brouwer fixed-point theorem for graph endomorphisms

DOI10.1186/1687-1812-2013-85zbMath1296.05136arXiv1206.0782OpenAlexW2115986395WikidataQ59304973 ScholiaQ59304973MaRDI QIDQ2249135

Oliver Knill

Publication date: 8 July 2014

Published in: Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.0782

zbMATH Keywords

Euler characteristicLefschetz numberdynamical zeta functionBrouwer fixed pointgraph endormorphisms

Mathematics Subject Classification ID

Small world graphs, complex networks (graph-theoretic aspects) (05C82) Random graphs (graph-theoretic aspects) (05C80) Stochastic network models in operations research (90B15) Fixed-point theorems (47H10) Planar graphs; geometric and topological aspects of graph theory (05C10) Index theory and related fixed-point theorems on manifolds (58J20) Relations of low-dimensional topology with graph theory (57M15) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Fixed points and coincidences in algebraic topology (55M20) Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) (05C60)

Related Items (4)

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Uses Software

• MathOverflow

Cites Work

• Fixed point theorems in \(\mathbb R\)-trees with applications to graph theory
• On periodic points
• A generalization of Brouwer's fixed point theorem
• Methods of Mathematical Economics
• Fixed-edge theorem for graphs with loops
• The Game of Hex and the Brouwer Fixed-Point Theorem
• Dynamical Zeta Functions for Piecewise Monotone Maps of the Interval
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