Solving maximum clique in sparse graphs: an \({O(nm+n2^{d/4})}\) algorithm for \(d\)-degenerate graphs

DOI10.1007/s11590-013-0698-2zbMath1303.05184OpenAlexW80045804MaRDI QIDQ479213

Austin Buchanan, Panos M. Pardalos, Jose L. Walteros, Sergiy I. Butenko

Publication date: 5 December 2014

Published in: Optimization Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11590-013-0698-2

zbMATH Keywords

degeneracymaximum cliquetractabilitysparse graphs\(d\)-degenerate graphsfixed-parameter

Mathematics Subject Classification ID

Programming involving graphs or networks (90C35) Graph algorithms (graph-theoretic aspects) (05C85) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69)

Related Items (5)

A polytime preprocess algorithm for the maximum independent set problem ⋮ Why Is Maximum Clique Often Easy in Practice? ⋮ A new decomposition technique for maximal clique enumeration for sparse graphs ⋮ General results on preferential attachment and clustering coefficient ⋮ Worst-case analysis of clique MIPs

Uses Software

• Algorithm 457

Cites Work

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• Number of cliques in random scale-free network ensembles
• Fast algorithms for max independent set
• Listing All Maximal Cliques in Sparse Graphs in Near-Optimal Time
• Smallest-last ordering and clustering and graph coloring algorithms
• Graph Partitioning and Graph Clustering
• k-Degenerate Graphs
• Algorithm 457: finding all cliques of an undirected graph

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