On the Minimum Feedback Vertex Set Problem: Exact and Enumeration Algorithms

We present a time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {O}(1.7548^{n})$\end{document} algorithm finding a minimum feedback vertex set in an undirected graph on n vertices. We also prove that a graph on n vertices can contain at most 1.8638n minimal feedback vertex sets and that there exist graphs having 105n/10≈1.5926n minimal feedback vertex sets.