importantSYS.SOURCE: arXiv• 2026-07-31T06:00:34Z

Efficient k-Coloring Algorithm Outperforms Chromatic Number Computation

#graph theory #algorithm optimization #complexity analysis #randomized algorithms #coloring problems

The paper presents a randomized algorithm for k-coloring n-vertex graphs with time complexity (2-ε_k)^n, improving upon the previous O*(2^n) method for computing the chromatic number. It combines techniques from list-coloring reductions and hypergraph-containers to achieve this result.

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> CURATED VIDEO PLATFORM LEVERAGING HACKER NEWS RECOMMENDATIONS > NES CONTRA (1987) NATIVE PORT VIA WEBASSEMBLY > CRITICAL LINUX IPV4 TCP USE-AFTER-FREE VULNERABILITY CVE-2026-98432 WITH CVSS 9.8 SEVERITY > RESPONSIBLE DISCLOSURE OF CPU SIDE-CHANNEL VULNERABILITIES AND ETHICAL RESPONSIBILITIES IN COMPUTER SECURITY > GPT-5.6 SOL COMPLETES PEACEFUL FACTORIO RUN IN 13.5 HOURS > MEMORY LATENCY'S IMPACT ON CPU UTILIZATION IN DATABASE GROUP BY OPERATIONS > THE IMPACT OF GENERATIVE AI ON CRITICAL THINKING: A SELF-REPORTED STUDY (2025)> WILLIAM NORDHAUS, NOBEL LAUREATE IN ECONOMICS, DIES AT 85 AFTER PIONEERING CLIMATE-ECONOMY RESEARCH > CYBERSECURITY BREACH EXPLOITS LED DISPLAY SOFTWARE VULNERABILITY ACROSS MULTIPLE COUNTRIES > US COPYRIGHT OFFICE CLARIFIES AI-GENERATED CONTENT COPYRIGHT ELIGIBILITY> CURATED VIDEO PLATFORM LEVERAGING HACKER NEWS RECOMMENDATIONS > NES CONTRA (1987) NATIVE PORT VIA WEBASSEMBLY > CRITICAL LINUX IPV4 TCP USE-AFTER-FREE VULNERABILITY CVE-2026-98432 WITH CVSS 9.8 SEVERITY > RESPONSIBLE DISCLOSURE OF CPU SIDE-CHANNEL VULNERABILITIES AND ETHICAL RESPONSIBILITIES IN COMPUTER SECURITY > GPT-5.6 SOL COMPLETES PEACEFUL FACTORIO RUN IN 13.5 HOURS > MEMORY LATENCY'S IMPACT ON CPU UTILIZATION IN DATABASE GROUP BY OPERATIONS > THE IMPACT OF GENERATIVE AI ON CRITICAL THINKING: A SELF-REPORTED STUDY (2025)> WILLIAM NORDHAUS, NOBEL LAUREATE IN ECONOMICS, DIES AT 85 AFTER PIONEERING CLIMATE-ECONOMY RESEARCH > CYBERSECURITY BREACH EXPLOITS LED DISPLAY SOFTWARE VULNERABILITY ACROSS MULTIPLE COUNTRIES > US COPYRIGHT OFFICE CLARIFIES AI-GENERATED CONTENT COPYRIGHT ELIGIBILITY