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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2512.21864 |
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| _version_ | 1866914221229342720 |
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| author | Gong, Simon Y. M. Wang, David G. L. Zhang, K. |
| author_facet | Gong, Simon Y. M. Wang, David G. L. Zhang, K. |
| contents | In this paper, we identify a new family of $e$-positive graphs, called the trinacria graphs $T_{(b+2)b2}$, thereby providing a partial answer to Stanley's question on which graphs are $e$-positive. The trinacria graph $T_{abc}$ is the graph on $a+b+c+3$ vertices obtained by attaching paths $P_a$, $P_b$ and~$P_c$ to the vertices of a triangle, respectively. Our proof relies on several ad hoc combinatorial ideas, and employs divide-and-conquer techniques, charging arguments, and progressive repair methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21864 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The trinacria graphs $T_{(b+2)b2}$ are $e$-positive Gong, Simon Y. M. Wang, David G. L. Zhang, K. Combinatorics In this paper, we identify a new family of $e$-positive graphs, called the trinacria graphs $T_{(b+2)b2}$, thereby providing a partial answer to Stanley's question on which graphs are $e$-positive. The trinacria graph $T_{abc}$ is the graph on $a+b+c+3$ vertices obtained by attaching paths $P_a$, $P_b$ and~$P_c$ to the vertices of a triangle, respectively. Our proof relies on several ad hoc combinatorial ideas, and employs divide-and-conquer techniques, charging arguments, and progressive repair methods. |
| title | The trinacria graphs $T_{(b+2)b2}$ are $e$-positive |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2512.21864 |