Real-rootedness of the $\tau$-polynomial under graph joins

Mingyang Kang, Zhixin Liu, Sophie C. C. Sun +1

For a simple graph $G$ with $n$ vertices, write its chromatic polynomial in the rising factorial basis as $${\chi }_G(x)=\sum _{i=0}^n(-1{)}^{n-i}{c}_i(G)⟨x{⟩}_i,$$ where $ \lan…