Simple factor graphs associated with split graphs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909978757955584 |
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| author | Pastine, Adrian Schvöllner, Victor Nicolas |
| author_facet | Pastine, Adrian Schvöllner, Victor Nicolas |
| contents | We introduce and study a loopless multigraph associated with a split graph $S$: the factor graph of $S$, denoted by $Φ(S)$, which encodes the combinatorial information about 2-switch transformations over $S$. This construction provides a cleaner, compact and non-redundant alternative to the graph $A_4(S)$ by Barrus and West, for the particular case of split graphs. If $Φ(S)$ is simple and connected, we obtain a precise description of the underlying structure of $S$, particularly when $Φ(S)$ is complete, highlighting the usefulness of the factor graph for understanding 2-switch dynamics in balanced and indecomposable split graphs, as well as its 2-switch-degree classification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24252 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simple factor graphs associated with split graphs Pastine, Adrian Schvöllner, Victor Nicolas Combinatorics We introduce and study a loopless multigraph associated with a split graph $S$: the factor graph of $S$, denoted by $Φ(S)$, which encodes the combinatorial information about 2-switch transformations over $S$. This construction provides a cleaner, compact and non-redundant alternative to the graph $A_4(S)$ by Barrus and West, for the particular case of split graphs. If $Φ(S)$ is simple and connected, we obtain a precise description of the underlying structure of $S$, particularly when $Φ(S)$ is complete, highlighting the usefulness of the factor graph for understanding 2-switch dynamics in balanced and indecomposable split graphs, as well as its 2-switch-degree classification. |
| title | Simple factor graphs associated with split graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2512.24252 |