Defective chromatic polynomials

Shamil Asgarli, Tamsen Whitehead McGinley, Nicholas Xue

For a graph $G$ and an integer $d\ge 0$, the defective chromatic polynomial $\ddot{I}{‡}_d(G;k)$ counts the $k$-colorings of $G$ in which each vertex has at most $d$ neighbors of its own c…