  In this paper we demonstrate that the property of monogamy of Bell violations
seen for no-signaling correlations in composite systems can be generalized to
the monogamy of contextuality in single systems obeying the Gleason property of
no-disturbance. We show how one can construct monogamies for contextual
inequalities by using the graph-theoretic technique of vertex decomposition of
a graph representing a set of measurements into subgraphs of suitable
independence numbers that themselves admit a joint probability distribution.
After establishing that all the subgraphs that are chordal graphs admit a joint
probability distribution, we formulate a precise graph-theoretic condition that
gives rise to the monogamy of contextuality. We also show how such monogamies
arise within quantum theory for a single four-dimensional system and interpret
violation of these relations in terms of a violation of causality. These
monogamies can be tested with current experimental techniques.
