School of Mathematics and Systems Science Shandong University Jinan 250100 China.;
Mathematics Department Tianjin Normal University Tianjin 300074 China.;
Institute of Software Chinese Academy of Sciences Beijing 100080 China.;
Dept.of Appl.Math. Changwon National Univ. Changwon 641-773 Korea.;
feedback vertex set; feedback edge set; tree-decomposition; tree-width; dynamic programming;