Word-Representability of Well-Partitioned Chordal Graphs
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913778482806784 |
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| author | Dwary, Tithi Krishna, K. V. |
| author_facet | Dwary, Tithi Krishna, K. V. |
| contents | In this paper, we study the word-representability of well-partitioned chordal graphs using split decomposition. We show that every component of the minimal split decomposition of a well-partitioned chordal graph is a split graph. Thus we have a characterization for word-representability of well-partitioned chordal graphs. As a consequence, we prove that the recognition of word-representability of well-partitioned chordal graphs can be done in polynomial time. Moreover, we prove that the representation number of a word-representable well-partitioned chordal graph is at most three. Further, we obtain a minimal forbidden induced subgraph characterization of circle graphs restricted to well-partitioned chordal graphs. Accordingly, we determine the class of word-representable well-partitioned chordal graphs having representation number exactly three. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04256 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Word-Representability of Well-Partitioned Chordal Graphs Dwary, Tithi Krishna, K. V. Combinatorics Discrete Mathematics In this paper, we study the word-representability of well-partitioned chordal graphs using split decomposition. We show that every component of the minimal split decomposition of a well-partitioned chordal graph is a split graph. Thus we have a characterization for word-representability of well-partitioned chordal graphs. As a consequence, we prove that the recognition of word-representability of well-partitioned chordal graphs can be done in polynomial time. Moreover, we prove that the representation number of a word-representable well-partitioned chordal graph is at most three. Further, we obtain a minimal forbidden induced subgraph characterization of circle graphs restricted to well-partitioned chordal graphs. Accordingly, we determine the class of word-representable well-partitioned chordal graphs having representation number exactly three. |
| title | Word-Representability of Well-Partitioned Chordal Graphs |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2504.04256 |