Fully leafed induced subtrees
Alexandre Blondin Mass\'e, Julien de Carufel, Alain Goupil, M\'elodie, Lapointe, \'Emile Nadeau, \'Elise Vandomme

TL;DR
This paper investigates the problem of finding induced subtrees with a specified number of vertices and leaves in a graph, establishing NP-completeness, analyzing specific graph families, and proposing algorithms for computation.
Contribution
It proves NP-completeness of the LIS problem, computes leaf-maximization functions for certain graph families, and introduces algorithms for general graphs and trees.
Findings
LIS problem is NP-complete in general graphs
Computed $L_G(i)$ for hypercubic graphs $Q_d$ for $2 \\leq d \\leq 6$
Developed branch and bound algorithm for any graph and an efficient algorithm for trees with bounded degree.
Abstract
Let be a simple graph on vertices. We consider the problem LIS of deciding whether there exists an induced subtree with exactly vertices and leaves in . We study the associated optimization problem, that consists in computing the maximal number of leaves, denoted by , realized by an induced subtree with vertices, for . We begin by proving that the LIS problem is NP-complete in general and then we compute the values of the map for some classical families of graphs and in particular for the -dimensional hypercubic graphs , for . We also describe a nontrivial branch and bound algorithm that computes the function for any simple graph . In the special case where is a tree of maximum degree , we provide a time and space algorithm to compute…
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Taxonomy
TopicsAdvanced Graph Theory Research · Interconnection Networks and Systems · Graph theory and applications
