Koana, Tomohiro
[Author];
Komusiewicz, Christian
[Author];
Sommer, Frank
[Author]
;
Tomohiro Koana and Christian Komusiewicz and Frank Sommer
[Contributor]
Exploiting c-Closure in Kernelization Algorithms for Graph Problems
Footnote:
Diese Datenquelle enthält auch Bestandsnachweise, die nicht zu einem Volltext führen.
Description:
A graph is c-closed if every pair of vertices with at least c common neighbors is adjacent. The c-closure of a graph G is the smallest number c such that G is c-closed. Fox et al. [SIAM J. Comput. '20] defined c-closure and investigated it in the context of clique enumeration. We show that c-closure can be applied in kernelization algorithms for several classic graph problems. We show that Dominating Set admits a kernel of size k^𝒪(c), that Induced Matching admits a kernel with 𝒪(c⁷ k⁸) vertices, and that Irredundant Set admits a kernel with 𝒪(c^{5/2} k³) vertices. Our kernelization exploits the fact that c-closed graphs have polynomially-bounded Ramsey numbers, as we show.