A BOUND ON THE PATHWIDTH OF SPARSE GRAPHS WITH APPLICATIONS TO EXACT ALGORITHMS

We present a bound of m/5.769 vertical bar O(log n) on the pathwidth of graphs with m edges. Respective path decompositions can be computed in polynomial time. Using a well-known framework for algorithms that rely on tree decompositions, this directly leads to runtime bounds of O*(2(m/5.769)) for Max-2SAT and Max-Cut. Both algorithms require exponential space due to dynamic programming. If we agree to accept a slightly larger bound of m/5.217 + 3, we even obtain path decompositions with a rather simple structure: all bags share a large set of common nodes. Using branching based algorithms, this allows us to solve the same problems in polynomial space and time O*(2(m/5.217)).