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arXiv · 2401.00323

Eulerian 2-Complexes

Richard H. Hammack·Paul C. Kainen
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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.

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Richard H. Hammack, Paul C. Kainen. 2023-12-30. Eulerian 2-Complexes. https://arxiv.org/abs/2401.00323

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