Representation Number of Word-Representable Split Graphs
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916708391845888 |
|---|---|
| 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. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00872 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Representation Number of Word-Representable Split 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. 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. |
| title | Representation Number of Word-Representable Split Graphs |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2502.00872 |