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- W2790492047 abstract "Abstract We show the close connection between the enumeration of cliques in a k-clique free graph G, the running time of DPLL-style algorithms for k-clique problem, and the length of tree-like resolution refutations for formula Clique ( G , k ) , which claims that G has a k-clique. The length of any such tree-like refutation is within a “fixed parameter tractable” factor from the number of cliques in the graph. We then proceed to drastically simplify the proofs of the lower bounds for the length of tree-like resolution refutations of Clique ( G , k ) shown in Beyersdorff et at. 2013, Lauria et al. 2017, which now reduce to a simple estimate of said quantity." @default.
- W2790492047 created "2018-03-29" @default.
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- W2790492047 date "2018-07-01" @default.
- W2790492047 modified "2023-09-23" @default.
- W2790492047 title "Cliques enumeration and tree-like resolution proofs" @default.
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- W2790492047 doi "https://doi.org/10.1016/j.ipl.2018.03.001" @default.
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