A Unified Approach for the Longest Path Problem on Some Tree-Like Graphs
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In a graph, a maximal biconnected component is called a block. A graph is called a block (resp., cactus and probe block) graph if its every block is a clique (resp., an edge or cycle, and complete split graph). In this paper, we propose a unified approach for the longest path problem on block, cactus, and probe block graphs. As a result, the longest path problem can be solved in linear time on block and probe block graphs, and in quadrat time on cactus graphs.
KeywordsLongest path problem Block graphs Cactus graphs Probe block graphs
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