  Plethysm is a fundamental operation in symmetric function theory, derived
directly from its connection with representation theory. However, it does not
admit a simple combinatorial interpretation, and finding coefficients of Schur
function plethysms is a major open question.
  In this paper, we introduce a graph-theoretic interpretation for any plethysm
based on the chromatic symmetric function. We use this interpretation to give
simple proofs of new and previously known plethystic identities, as well as
chromatic symmetric function identities.
