# A notion of graph homeomorphism

@article{Knill2014ANO, title={A notion of graph homeomorphism}, author={Oliver Knill}, journal={ArXiv}, year={2014}, volume={abs/1401.2819} }

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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