# A Unified Approach for the Longest Path Problem on Some Tree-Like Graphs

• Ang-Lin Dong
• Sheng-Lung Peng
Conference paper
Part of the Lecture Notes in Business Information Processing book series (LNBIP, volume 222)

## Abstract

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.

## Keywords

Longest path problem Block graphs Cactus graphs Probe block graphs

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