An Improved Deterministic Parameterized Algorithm for Cactus Vertex Deletion

A cactus is a connected graph that does not contain K4 − e as minor. Given G = (V,E) and an integer k ≥ 0, Cactus Vertex Deletion (also known Diamond Hitting Set) the problem of deciding whether has vertex set size at most whose removal leaves forest cacti. The previously best deterministic parameterized algorithm for this was due to Bonnet et al. [WG 2016], which runs in time 26knO(1), where n number vertices G. In paper, we design Deletion, 17.64knO(1). As almost straightforward application our algorithm, also give 17.64knO(1)-time Even Cycle Transversal, improves previous running 50knO(1) Misra 2012].