Characterization of Split Comparability Graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909595671199744 |
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| author | Dwary, Tithi Mozhui, Khyodeno Krishna, K. V. |
| author_facet | Dwary, Tithi Mozhui, Khyodeno Krishna, K. V. |
| contents | A split graph is a graph whose vertex set can be partitioned into a clique and an independent set. A split comparability graph is a split graph which is transitively orientable. In this work, we characterize split comparability graphs in terms of vertex labelling. Further, using this characterization, we prove that the permutation-representation number of a split comparability graph is at most three. This gives us an alternative proof of the result in order theory that the dimension of a split order is at most three. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_19167 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterization of Split Comparability Graphs Dwary, Tithi Mozhui, Khyodeno Krishna, K. V. Combinatorics Discrete Mathematics A split graph is a graph whose vertex set can be partitioned into a clique and an independent set. A split comparability graph is a split graph which is transitively orientable. In this work, we characterize split comparability graphs in terms of vertex labelling. Further, using this characterization, we prove that the permutation-representation number of a split comparability graph is at most three. This gives us an alternative proof of the result in order theory that the dimension of a split order is at most three. |
| title | Characterization of Split Comparability Graphs |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2504.19167 |