Characterization of Split Comparability Graphs
Combinatorics
2025-04-29 v1 Discrete Mathematics
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.
Keywords
Cite
@article{arxiv.2504.19167,
title = {Characterization of Split Comparability Graphs},
author = {Tithi Dwary and Khyodeno Mozhui and K. V. Krishna},
journal= {arXiv preprint arXiv:2504.19167},
year = {2025}
}