arXiv Open Access 2025

Representation Number of Word-Representable Split Graphs

Tithi Dwary Khyodeno Mozhui K. V. Krishna
Lihat Sumber

Abstrak

A split graph is a graph whose vertex set can be partitioned into a clique and an independent set. The word-representability of split graphs was studied in a series of papers in the literature, and the class of word-representable split graphs was characterized through semi-transitive orientation. Nonetheless, the representation number of this class of graphs is still not known. In general, determining the representation number of a word-representable graph is an NP-complete problem. In this work, through an algorithmic procedure, we show that the representation number of the class of word-representable split graphs is at most three. Further, we characterize the class of word-representable split graphs as well as the class of split comparability graphs which have representation number exactly three.

Topik & Kata Kunci

Penulis (3)

T

Tithi Dwary

K

Khyodeno Mozhui

K

K. V. Krishna

Format Sitasi

Dwary, T., Mozhui, K., Krishna, K.V. (2025). Representation Number of Word-Representable Split Graphs. https://arxiv.org/abs/2502.00872

Akses Cepat

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Informasi Jurnal
Tahun Terbit
2025
Bahasa
en
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arXiv
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Open Access ✓