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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.00110 |
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| _version_ | 1866914938443792384 |
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| author | Talbot, John Yan, Jun |
| author_facet | Talbot, John Yan, Jun |
| contents | A simple graph is triangular if every edge is contained in a triangle. A sequence of integers is graphical if it is the degree sequence of a simple graph. Egan and Nikolayevsky recently conjectured that every graphical sequence whose terms are all at least 4 is the degree sequence of a triangular simple graph, and proved this in some special cases. In this paper we state and prove the analogous version of this conjecture for multigraphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_00110 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Degree sequences of triangular multigraphs Talbot, John Yan, Jun Combinatorics 05C07 A simple graph is triangular if every edge is contained in a triangle. A sequence of integers is graphical if it is the degree sequence of a simple graph. Egan and Nikolayevsky recently conjectured that every graphical sequence whose terms are all at least 4 is the degree sequence of a triangular simple graph, and proved this in some special cases. In this paper we state and prove the analogous version of this conjecture for multigraphs. |
| title | Degree sequences of triangular multigraphs |
| topic | Combinatorics 05C07 |
| url | https://arxiv.org/abs/2311.00110 |