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arXiv · 2508.19453

Asymptotic size of the Karp-Sipser Core in Configuration Model

Arnab Chatterjee·Joon Hyung Lee·Haodong Zhu
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Abstract

We study the asymptotic size of the Karp-Sipser core in the configuration model with arbitrary degree distributions. The Karp-Sipser core is the induced subgraph obtained by iteratively removing all leaves and their neighbors through the leaf-removal process, and finally discarding any isolated vertices \cite{BCC}. Our main result establishes the convergence of the Karp-Sipser core size to an explicit fixed-point equation under general degree assumptions.The approach is based on analyzing the corresponding local weak limit of the configuration model - a unimodular Galton-Watson tree and tracing the evolution process of all vertex states under leaf-removal dynamics by use of the working mechanism of an enhanced version of Warning Propagation along with Node Labeling Propagation.

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Arnab Chatterjee, Joon Hyung Lee, Haodong Zhu. 2025-08-26. Asymptotic size of the Karp-Sipser Core in Configuration Model. https://arxiv.org/abs/2508.19453

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