  We show that the perfect commutation graph is the sufficient tight condition
for admitting the noncontextual description of each observable set satisfying
it in the yes-no question scenario. With this condition, we propose a method
for proving the monogamy relation between two informationtheoretic
contextuality inequalities by decomposing the total commutation graph into
perfect subgraphs. The results offer a powerful tool to investigate the
contextuality and to understand quantum information theory. This theoretical
work can be experimentally verified in current laboratorial technology.
