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A notion of graph homeomorphism

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arxiv 1401.2819 v1 pith:NCV6HN2G submitted 2014-01-13 math.GN cs.DM

Oliver Knill This is my paper · ORCID
classification math.GNcs.DM
keywords fixedgraphdimensionhomeomorphismhomotopynotionpointbrouwer-lefshetz
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We introduce a notion of graph homeomorphisms which uses the concept of dimension and homotopy for graphs. It preserves the dimension of a subbasis, cohomology and Euler characteristic. Connectivity and homotopy look as in classical topology. The Brouwer-Lefshetz fixed point leads to the following discretiszation of the Kakutani fixed point theorem: any graph homeomorphism T with nonzero Lefschetz number has a nontrivial invariant open set which is fixed by T.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Dehn Sommerville Manifolds

    math.CO 2025-08 reject novelty 6.0 of 10

    Dehn-Sommerville manifolds form a broad class of finite simplicial complexes that the paper claims to endow with Dehn-Sommerville face symmetries, level-set closure, chromatic bound 2q+2, and monoid closure under joins.

  2. Euler Characteristics of Random Manifolds

    math.CO 2026-07 conditional novelty 5.0 of 10

    For a random codimension-1 level set H in a simplicial complex G, E[χ(H)] equals 2−2K(G)−χ(G), with K the curvature functional built from the f-vector.

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