New Analytical Lower Bounds On The Clique Number Of A Graph

This paper proposes three new analytical lower bounds on the clique number of a graph and compares these bounds with those previously established in the literature. Two proposed bounds are derived from the well-known Motzkin–Straus quadratic programming formulation for the maximum clique problem. Theoretical results on the comparison of various bounds are established. Computational experiments are performed on random graph models such as the Erdös-Rényi model for uniform graphs and the generalized random graph model for power-law graphs that simulate graphs with different densities and assortativity coefficients. Computational results suggest that the proposed new analytical bounds improve the existing ones on many graph instances