Reproduce “SSD Set System, Graph Decomposition and Hamiltonian Cycle” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Kan Shota, Kazuya Haraguchi
Researchers at Kyoto University introduce Superset-Subset-Disjoint (SSD) set systems, a generalization of prior frameworks, to characterize properties like k-edge-connectivity in graphs. This theoretical foundation enables an $O(n+m)$ delay algorithm for enumerating strongly-connected induced subgraphs, and provides a new sufficient condition for Hamiltonian cycles in directed graphs.
Key insights
- The novel SSD set system provides a more general theoretical framework capable of characterizing properties like k-edge-connectivity in graphs.
- Any solution within an SSD system is either MaxPSS-disjoint and/or MinRS-disjoint, which leads to a unique, canonical graph decomposition.
- Dominator trees are instrumental in efficiently characterizing and generating minimal removable sets (MinRSs) in strongly-connected digraphs.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.