A notion of graph homeomorphism
Abstract
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 BrouwerLefshetz 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.
 Publication:

arXiv eprints
 Pub Date:
 January 2014
 arXiv:
 arXiv:1401.2819
 Bibcode:
 2014arXiv1401.2819K
 Keywords:

 Mathematics  General Topology;
 Computer Science  Discrete Mathematics;
 05C75;
 54A99;
 57M15;
 55M10;
 55M20
 EPrint:
 11 figures, 33 pages