An Improved Deterministic Parameterized Algorithm for Cactus Vertex Deletion

A cactus is a connected graph that does not contain K 4 − e as a minor. Given a graph G = ( V , E ) and an integer k ≥ 0, Cactus Vertex Deletion (also known as Diamond Hitting Set ) is the problem of deciding whether G has a vertex set of size at most k whose removal leaves a forest of cacti. The previously best deterministic parameterized algorithm for this problem was due to Bonnet et al. [WG 2016 ], which runs in time 26 k n O (1) , where n is the number of vertices of G . In this paper, we design a deterministic algorithm for Cactus Vertex Deletion , which runs in time 17.64 k n O (1) . As an almost straightforward application of our algorithm, we also give a deterministic 17.64 k n O (1) -time algorithm for Even Cycle Transversal , which improves the previous running time 50 k n O (1) of the known deterministic parameterized algorithm due to Misra et al. [WG 2012 ].