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Longest \((s, t)\)-paths in \(L\)-shaped grid graphs. (English) Zbl 1414.05164
Summary: The longest path problem, that is, finding a simple path with the maximum number of vertices, is a well-known NP-hard problem with many applications. However, for some classes of graphs, including solid grid graphs and grid graphs with some holes, it is open. An \(L\)-shaped grid graph is a special kind of a rectangular grid graph with a rectangular hole. In this paper, we show that a longest path between two given vertices \(s\) and \(t\) of an \(L\)-shaped grid graph can be computed in linear time.

05C38 Paths and cycles
05C12 Distance in graphs
68R10 Graph theory (including graph drawing) in computer science
Full Text: DOI
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