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arXiv · 2504.19167

Characterization of Split Comparability Graphs

Tithi Dwary·Khyodeno Mozhui·K. V. Krishna
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Abstract

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.

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Tithi Dwary, Khyodeno Mozhui, K. V. Krishna. 2025-04-27. Characterization of Split Comparability Graphs. https://arxiv.org/abs/2504.19167

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