  In 1990, Kostochka and Sidorenko proposed studying the smallest number of
list-colorings of a graph $G$ among all assignments of lists of a given size
$n$ to its vertices. We say a graph $G$ is $n$-monophilic if this number is
minimized when identical $n$-color lists are assigned to all vertices of $G$.
Kostochka and Sidorenko observed that all chordal graphs are $n$-monophilic for
all $n$. Donner (1992) showed that every graph is $n$-monophilic for all
sufficiently large $n$. We prove that all cycles are $n$-monophilic for all
$n$; we give a complete characterization of 2-monophilic graphs (which turns
out to be similar to the characterization of 2-choosable graphs given by Erdos,
Rubin, and Taylor in 1980); and for every $n$ we construct a graph that is
$n$-choosable but not $n$-monophilic.
