See if you can determine this in polynomial time. The problem is also relevent for covering graph of other classes, such as N-free or interval orders. Open problems include recognition, optimization, counting, representation. Optimization Requiring Representation Find any example of a problem which is NP-complete on a class of graphs if the input is in adjacency list form, and polynomial if the class is given with its natural representation. Recognition Famous open problem, not known to be in NP, still open if you are given the ordering of points on the boundary of the polygon.
All problems above are still open, as are some others.
Contains chordal bipartite graphs. Apparently, almost nothing is known about the intersection graphs of circles in the plane, so recognition, structural characterization, and representation problems are all open. These graphs include among other classes the chordal graphs and circular-arc graphs. Forbidden Submatrices Consider matrices which can be permuted to avoid a specific submatrix. A well covered graph is a graph in which every maximal independent set is maximum.