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English version:
Journal of Applied and Industrial Mathematics, 2016, 10:1, 1-6

Volume 23, No 1, 2016, P. 5-16

UDC 519.17
V. E. Alekseev and D. V. Zakharova
Independent sets in graphs without subtrees with many leaves

Abstract:
A subtree of a graph is called inscribed if there is no three vertices in the subtree inducing a triangle in the graph. We prove that for any fixed k the independent set problem is solvable in polynomial time for each of the following classes of graphs: 1) the graphs without subtrees with k leaves, 2) the subcubic graphs without inscribed subtrees with k leaves, 3) the graphs with degrees not exceeding k without induced subtrees with 4 leaves.
Ill. 1, bibliogr. 12.

Keywords: graph, independent set, forbidden subtree, polynomial algorithm.

DOI: 10.17377/daio.2016.23.499

Vladimir E. Alekseev 1
Darya V. Zakharova 1

1. Nizhniy Novgorod State University,
23 Gagarin Ave., 603950 Nizhniy Novgorod, Russia
e-mail: aleve@rambler.ru, dvzakh@rambler.ru

Received 11 June 2015
Revised 25 June 2015

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 © Sobolev Institute of Mathematics, 2015