digraphs – Optimization Online

Kernels in planar digraphs

Published: 2004/06/18

Graphs and Matroids digraphs, fpt, kernels

A set $S$ of vertices in a digraph $D=(V,A)$ is a kernel if $S$ is independent and every vertex in $V-S$ has an out-neighbor in $S$. We show that there exist $O(n2^{19.1 \sqrt{k}}+n^4)$-time and $O(2^{19.1 \sqrt{k}} k^9 + n^2)$-time algorithms for checking whether a planar digraph $D$ of order $n$ has a kernel with at … Read more

Kernels in planar digraphs

Published: 2001/05/21

Gregory Gutin

Ton Kloks

Chuan Min Lee

Graphs and Matroids digraphs, ftp, kernels

A set $S$ of vertices in a digraph $D=(V,A)$ is a kernel if $S$ is independent and every vertex in $V-S$ has an out-neighbour in $S$. We show that there exists an $O(3^{\delta \sqrt{k}} n)$~% \footnote{Throughout this paper the constants $\delta$ and $c$ are the same as the comparative constants mentioned in~\cite{kn:alber}.} algorithm to check … Read more