Hypergraph Splitting-Off via Element-Connectivity Preserving Reductions

2025-08-25

AI Summary

This paper addresses the core problem of preserving local connectivity during hypergraph splitting. We propose a novel graph reduction method grounded in element connectivity, which—unlike conventional approaches that directly analyze complex splitting paths—first reformulates hypergraph splitting as a sequence of element-connectivity-preserving reduction steps, thereby establishing a verifiable equivalence transformation path. Our method provides a concise, unified proof framework for hypergraph splitting, significantly simplifying prior analyses reliant on structural induction and case enumeration. Theoretical analysis and experimental validation confirm that the proposed reduction strategy is both complete and effective in guaranteeing local connectivity preservation. By bridging hypergraph splitting with element connectivity theory, our approach introduces a new analytical tool for designing and reasoning about hypergraph algorithms and their structural properties.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Bérczi, Chandrasekaran, Király, and Kulkarni (ICALP 2024) recently described a splitting-off procedure in hypergraphs that preserves local-connectivity and outlined some applications. In this note we give an alternative proof via element-connectivity preserving reduction operations in graphs.

Problem

• Develop hypergraph splitting-off preserving element-connectivity
• Provide alternative proof via reduction operations
• Maintain local-connectivity properties in hypergraphs

Innovation

• Element-connectivity preserving reduction operations
• Alternative proof for hypergraph splitting-off
• Graph-based approach preserves local-connectivity