Abstract
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.
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Original Russian Text © V.E. Alekseev, D.V. Zakharova, 2016, published in Diskretnyi Analiz i Issledovanie Operatsii, 2016, Vol. 23, No. 1, pp. 5–14.
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Alekseev, V.E., Zakharova, D.V. Independent sets in graphs without subtrees with many leaves. J. Appl. Ind. Math. 10, 1–6 (2016). https://doi.org/10.1134/S1990478916010014
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DOI: https://doi.org/10.1134/S1990478916010014