Turán's Theorem Through Algorithmic Lens
14 July 2023
Data Structures and Algorithms
Fedor V. Fomin,
Petr A. Golovach,
A new compression reduces finding cliques above Turan's bound to maximum clique on 5k vertices
This gives an FPT algorithm for finding cliques above Turan's bound, with running time 2.49^k(n+m)
The paper also gives an FPT algorithm for finding large independent sets above Turan's bound in bounded average degree graphs
The dependence of the algorithms on parameters is shown to be tight under ETH
The paper links extremal graph theory and algorithms in a new way
Finding large cliques in sparse graphs
This paper develops a compression algorithm that reduces the problem of finding a clique of size l in a sparse n-vertex graph to finding a maximum clique in a graph of size about 5k. This yields an FPT algorithm for finding cliques above Turan's bound, with running time 2.49^k(n+m). The paper also gives an algorithm for finding large independent sets above Turan's bound in graphs of bounded average degree.
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