Upper Embeddability of Graphs and Products of Transpositions Associated with Edges
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866913296010969088 |
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| author | Tsujie, Shuhei Uchiumi, Ryo |
| author_facet | Tsujie, Shuhei Uchiumi, Ryo |
| contents | Given a graph, we associate each edge with the transposition which exchanges the endvertices. Fixing a linear order on the edge set, we obtain a permutation of the vertices. Dénes proved that the permutation is a full cyclic permutation for any linear order if and only if the graph is a tree.
In this article, we characterize graphs having a linear order such that the associated permutation is a full cyclic permutation in terms of graph embeddings. Moreover, we give a counter example for Eden's question about an edge ordering whose associated permutation is the identity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_05422 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Upper Embeddability of Graphs and Products of Transpositions Associated with Edges Tsujie, Shuhei Uchiumi, Ryo Combinatorics 05C25, 05C10, 57M15 Given a graph, we associate each edge with the transposition which exchanges the endvertices. Fixing a linear order on the edge set, we obtain a permutation of the vertices. Dénes proved that the permutation is a full cyclic permutation for any linear order if and only if the graph is a tree. In this article, we characterize graphs having a linear order such that the associated permutation is a full cyclic permutation in terms of graph embeddings. Moreover, we give a counter example for Eden's question about an edge ordering whose associated permutation is the identity. |
| title | Upper Embeddability of Graphs and Products of Transpositions Associated with Edges |
| topic | Combinatorics 05C25, 05C10, 57M15 |
| url | https://arxiv.org/abs/2211.05422 |