Abstract
In the k-Vertex-Disjoint Paths problem, we are given a graph G and k terminal pairs of vertices, and are asked whether there is a set of k vertex-disjoint paths linking these terminal pairs, respectively. In the k-Path problem, we are given a graph and are asked whether there is a path of length k. It is known that both problems are NP-hard even in split graphs, which are the graphs whose vertices can be partitioned into a clique and an independent set. We study kernelization for the two problems in split graphs. In particular, we derive a 4k vertex-kernel for the k-Vertex-Disjoint Paths problem and a 3/2k2+ ½k vertex-kernel for the k-Path problem.
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CITATION STYLE
Yang, Y., Shrestha, Y. R., Li, W., & Guo, J. (2016). Kernelization of two path searching problems on split graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9711, pp. 238–249). Springer Verlag. https://doi.org/10.1007/978-3-319-39817-4_23
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