Refined notions of parameterized enumeration kernels with applications to matching cut enumeration

An enumeration kernel as defined by Creignou et al. (2017) [11] for a parameterized problem consists of an algorithm that transforms each instance into one whose size is bounded the parameter plus solution-lifting efficiently enumerates all solutions from set kernel. We propose to consider two new versions kernels asking original can be enumerated in polynomial time or with delay solutions. Using NP-hard Matching Cut structural parameters such vertex cover number cyclomatic input graph, we show present useful notion data reduction problems which allows compactly represent feasible