New Analytical Lower Bounds On The Clique Number Of A Graph
Keywords
assortativity coefficient; clique number; Erdös-Rényi model; Motzkin–Straus formulation; power-law graphs; spectral graph theory
Abstract
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.
Publication Date
3-4-2017
Publication Title
Optimization Methods and Software
Volume
32
Issue
2
Number of Pages
336-368
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1080/10556788.2016.1172578
Copyright Status
Unknown
Socpus ID
84965057371 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/84965057371
STARS Citation
Stozhkov, Vladimir; Pastukhov, Grigory; Boginski, Vladimir; and Pasiliao, Eduardo L., "New Analytical Lower Bounds On The Clique Number Of A Graph" (2017). Scopus Export 2015-2019. 5730.
https://stars.library.ucf.edu/scopus2015/5730