Eulerian 2-Complexes
Combinatorics
2024-01-02 v1
Abstract
It is shown that Euler's theorem for graphs can be generalized for 2-complexes. Two notions that generalize cycle and Eulerian tour are introduced (``circlet'' and ``Eulerian cover''), and we show that for a strongly-connected, pure 2-complex, the following are equivalent: (i) each edge meets a positive even number of 2-cells (faces), (ii) the complex can be decomposed as the face-disjoint union of circlets, and (iii) the complex has an Eulerian cover. A number of examples are provided.
Cite
@article{arxiv.2401.00323,
title = {Eulerian 2-Complexes},
author = {Richard H. Hammack and Paul C. Kainen},
journal= {arXiv preprint arXiv:2401.00323},
year = {2024}
}
Comments
13 pages, 15 figures