Many exact search algorithms for NP-hard graph problems adopt the old Davis-Putman branch-and-reduce paradigm. The performance of these algorithms often suffers from the increasing number of graph modifications, such as vertex/edge deletions, that reduce the problem instance and have to be "taken back" frequently during the search process. We investigate practical implementation-based aspects of exact graph algorithms by providing a simple hybrid graph representation that trades space for time to address the said take-back challenge. Experiments on three well studied problems show consistent significant improvements over classical methods.