Eulerian 2-Complexes
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916078132658176 |
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| author | Hammack, Richard H. Kainen, Paul C. |
| author_facet | Hammack, Richard H. Kainen, Paul C. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00323 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Eulerian 2-Complexes Hammack, Richard H. Kainen, Paul C. Combinatorics 57Q35, 05C40 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. |
| title | Eulerian 2-Complexes |
| topic | Combinatorics 57Q35, 05C40 |
| url | https://arxiv.org/abs/2401.00323 |