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.

翻译：参数化枚举问题的枚举核化由Creignou等人[Theory Comput. Syst. 2017]提出，后经Golovach等人[J. Comput. Syst. Sci. 2022, STACS 2021]精炼为多项式延迟枚举核化。本文从枚举核化角度研究ENUM LONG-PATH——长路径问题的枚举变体。形式化定义如下：给定无向图G和整数k，ENUM LONG-PATH的目标是枚举G中所有恰好包含k个顶点的路径。我们针对顶点覆盖数、解离数及到团距离这三类结构参数，分别为每个参数构建了具有多项式规模的多项式延迟枚举核。