The Almost Induced Matching problem asks whether we can delete at most k vertices from the input graph such that each vertex in the remaining graph has a degree exactly one. This paper studies parameterized algorithms for this problem by taking the size k of the deletion set as the parameter. We give a 7k-vertex kernel and an $O^{⁎}({1.7485}^k)$-time and polynomial-space algorithm, both of which are the best-known results. The linear-vertex kernel is obtained by using an extended crown decomposition and careful analysis, and the parameterized algorithm is based on a branch-and-search paradigm.

中文翻译：

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用于几乎诱导匹配的参数化算法和内核

在几乎导出匹配问题，询问是否可以最多删除ķ顶点从输入图形，使得在剩余图中每个顶点有且只有一个学位。本文以删除集的大小k为参数，研究了针对该问题的参数化算法。我们给出了一个7 k -vertex内核和一个${Ø}^{⁎}（{1.7485}^{ķ}）$时间和多项式空间算法，两者都是最著名的结果。线性顶点核是通过使用扩展的Crown分解和仔细的分析而获得的，而参数化算法则基于分支搜索范式。