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

2025/12/26 by Simon Y. M. Gong, David G. L. Wang, Gong, Simon Y. M. +3
Computer Science · #Interconnection Networks and Systems #Advanced Graph Theory Research #Computational Geometry and Mesh Generation

paper · doi:10.48550/arxiv.2512.21864

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.

Citations

• The chromatic symmetric function of graphs glued at a single vertex
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• Noncommutative symmetric functions

Related

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