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arXiv · 1310.5786

Contracting Graphs to Split Graphs and Threshold Graphs

Leizhen Cai·Chengwei Guo
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Abstract

We study the parameterized complexity of Split Contraction and Threshold Contraction. In these problems we are given a graph G and an integer k and asked whether G can be modified into a split graph or a threshold graph, respectively, by contracting at most k edges. We present an FPT algorithm for Split Contraction, and prove that Threshold Contraction on split graphs, i.e., contracting an input split graph to a threshold graph, is FPT when parameterized by the number of contractions. To give a complete picture, we show that these two problems admit no polynomial kernels unless NP\subseteq coNP/poly.

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Leizhen Cai, Chengwei Guo. 2013-10-22. Contracting Graphs to Split Graphs and Threshold Graphs. https://arxiv.org/abs/1310.5786

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