### Faster Fixed Parameter Tractable Algorithms for Undirected Feedback Vertex Set [chapter]

Venkatesh Raman, Saket Saurabh, C. R. Subramanian
<span title="">2002</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
A feedback vertex set (fvs) of a graph is a set of vertices whose removal results in an acyclic graph. We show that if an undirected graph on n vertices with minimum degree at least 3 has a fvs on at most 1 3 n 1− vertices, then there is a cycle of length at most 6 (for ≥ 1/2, we can even improve this to just 6). Using this, we obtain a O(( 12 log k log log k + 6) k n ω ) algorithm for testing whether an undirected graph on n vertices has a fvs of size at most k. Here n ω is the complexity of
more &raquo; ... e best matrix multiplication algorithm. The previous best parameterized algorithm for this problem took O((2k + 1) k n 2 ) time. We also investigate the fixed parameter complexity of weighted feedback vertex set problem in weighted undirected graphs.
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