Polynomial-Size Enumeration Kernelizations for Long Path Enumeration
Discrete Mathematics
2025-03-03 v1
Abstract
Enumeration kernelization for parameterized enumeration problems was defined by Creignou et al. [Theory Comput. Syst. 2017] and was later refined by Golovach et al. [J. Comput. Syst. Sci. 2022, STACS 2021] to polynomial-delay enumeration kernelization. We consider ENUM LONG-PATH, the enumeration variant of the Long-Path problem, from the perspective of enumeration kernelization. Formally, given an undirected graph G and an integer k, the objective of ENUM LONG-PATH is to enumerate all paths of G having exactly k vertices. We consider the structural parameters vertex cover number, dissociation number, and distance to clique and provide polynomial-delay enumeration kernels of polynomial size for each of these parameters.
Cite
@article{arxiv.2502.21164,
title = {Polynomial-Size Enumeration Kernelizations for Long Path Enumeration},
author = {Christian Komusiewicz and Diptapriyo Majumdar and Frank Sommer},
journal= {arXiv preprint arXiv:2502.21164},
year = {2025}
}