Characterization of Split Comparability Graphs

Fuente: arXiv
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Main Authors: Dwary, Tithi, Mozhui, Khyodeno, Krishna, K. V.
Format: Preprint
Published: 2025
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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
id 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