On the maxima of Motzkin-Straus programs and cliques of graphs

DOI10.1007/s10898-022-01187-3zbMath1500.05026OpenAlexW4281753273MaRDI QIDQ2089888

Cheng Zhao, Peng Zhao, Qing-song Tang, Xiang-De Zhang

Publication date: 24 October 2022

Published in: Journal of Global Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10898-022-01187-3

zbMATH Keywords

quadratic programcliques of graphsLagrangian of graphsMotzkin-Straus program

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Nonlinear programming (90C30) Hypergraphs (05C65) Combinatorial optimization (90C27) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69) Extremal combinatorics (05D99)

Uses Software

• Mathematica
• QUALEX

Cites Work

• Linear and nonlinear programming.
• Evolution towards the maximum clique
• Exact bounds on the order of the maximum clique of a graph.
• A new trust region technique for the maximum weight clique problem
• A global optimization approach for solving the maximum clique problem
• Continuous Characterizations of the Maximum Clique Problem
• Turan's Graph Theorem
• A General Regularized Continuous Formulation for the Maximum Clique Problem
• A Continuous-Based Approach for Partial Clique Enumeration
• Maxima for Graphs and a New Proof of a Theorem of Turán
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