An Improved Kernel and Parameterized Algorithm for Almost Induced Matching

An induced subgraph is called an induced matching if each vertex is a degree-1 vertex in the subgraph. The Almost Induced Matching problem asks whether we can delete at most k vertices from the input graph such that the remaining graph is an induced matching. This paper studies parameterized algorithms for this problem by taking the size k of the deletion set as the parameter. First, we prove a 6k-vertex kernel for this problem, improving the previous result of 7k. Second, we give an \(O^*(1.6765^k)\) -time and polynomial-space algorithm, improving the previous running-time bound of \(O^*(1.7485^k)\) .