Max-leaves spanning tree is APX-hard for cubic graphs
MaxLeaf is the problem of finding a spanning tree with a maximum number of leaves in a connected graph. \textit{R. Solis-Oba} [Lect.\ Notes Comput. Sci. 1461, 441--452 (1998; Zbl 0932.68069)] presented a 2-approximation algorithm for MaxLeaf. \textit{P. Bonsma} and \textit{F. Zickfeld} [SIAM J.\ Discrete Math.\ 25, No.\ 4, 1652--1666 (2011; Zbl 1237.05041)] gave a 3/2-approximation algorithm for the restriction to cubic graphs. \textit{G. Galbiati}, \textit{F. Maffioli} and \textit{A. Morzenti} [Inf. Process. Lett. 52, No. 1, 45--49 (1994; Zbl 0942.68647)] showed that MaxLeaf is APX-hard in general. Here the author shows that MaxLeaf is also APX-hard for cubic graphs, and so is the related problem Minimum Connected Dominating Set when restricted to cubic graphs.
scientific article; zbMATH DE number 6033184
scientific article