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arXiv · 2502.21164

Polynomial-Size Enumeration Kernelizations for Long Path Enumeration

Christian Komusiewicz·Diptapriyo Majumdar·Frank Sommer
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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.

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Christian Komusiewicz, Diptapriyo Majumdar, Frank Sommer. 2025-02-28. Polynomial-Size Enumeration Kernelizations for Long Path Enumeration. https://arxiv.org/abs/2502.21164

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