  We propose a class of new cutting planes to strengthen the Lov\'asz theta
function, a well-known semidefinite programming (SDP) relaxation for the stable
set and the graph coloring problems. For both problems, we introduce two new
cutting planes that are derived from odd-cycle constraints and triangle
inequalities and are valid for certain subgraphs induced by odd cycles.
Computational experiments on graphs from the literature show that for each
problem, one of the proposed cutting planes gives very good bounds.
