3 problems

Let $G=(V,E)$ be a triangle-free graph of average degree $d$, let $Z_G(\lambda)$ denote its independence polynomial, and let $W$ be the Lambert $W$-function, defined by…

Let $G=(V,E)$ be a triangle-free graph of average degree $d$, let $Z_G(\lambda)$ denote its independence polynomial, and write $Z_G'(1)$ for its derivative at $1$. Occupancy-fracti…

For each integer $\Delta\geq 3$, let $\mathcal{G}_\Delta$ be the class of graphs of maximum degree at most $\Delta$, and let … where $Z_G(\lambda)$ is the independence polynomial o…