Independent sets in graphs without subtrees with many leaves
- 19 Downloads
A subtree of a graph is called inscribed if no three vertices of the subtree generate a triangle in the graph. We prove that, for fixed k, the independent set problem is solvable in polynomial time for each of the following classes of graphs: (1) graphs without subtrees with k leaves, (2) subcubic graphs without inscribed subtrees with k leaves, and (3) graphs with degree not exceeding k and lacking induced subtrees with four leaves.
Keywordsgraph independent set forbidden subtree polynomial algorithm
Unable to display preview. Download preview PDF.
- 4.V. E. Alekseev and V. A. Talanov, Graphs and Algorithms. Data Structures. Computation Models (Internet-Univ. Inform. Tekhnol., BINOM. Lab. Znanii,Moscow, 2006) [in Russian].Google Scholar
- 8.D. S. Malyshev, “Classes ofSubcubicPlanarGraphs forWhich the Independent Set Problem Is Polynomially Solvable,” Diskret. Anal. Issled. Oper. 20 (3), 26–44 (2013) [J. Appl. Indust. Math. 7 (4), 537–548 2013].Google Scholar
- 12.D. V. Zakharova, “Weighted Independent Sets in Graphs with Bounded Minors of the Extended Incidence Matrix,” in Proceedings of the X InternationalWorkshop “Discrete Mathematics and Its Applications”, January 1–6, 2010, Moscow, Russia (Mekh.-Mat. Fak., Moskov. Gos. Univ., Moscow, 2010), pp. 303–305.Google Scholar