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arXiv · 2512.21864

The trinacria graphs $T_{(b+2)b2}$ are $e$-positive

Simon Y. M. Gong·David G. L. Wang·K. Zhang
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Abstract

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.

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Simon Y. M. Gong, David G. L. Wang, K. Zhang. 2025-12-26. The trinacria graphs $T_{(b+2)b2}$ are $e$-positive. https://arxiv.org/abs/2512.21864

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