Theoretical Computer Science ( IF 0.747 ) Pub Date : 2020-09-15 , DOI: 10.1016/j.tcs.2020.09.026
Mingyu Xiao; Shaowei Kou

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 ${O}^{⁎}\left({1.7485}^{k}\right)$-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.

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