Recognition of Linear and Star Variants of Leaf Powers is in P
Data Structures and Algorithms
2022-03-10 v2 Combinatorics
Abstract
A -leaf power of a tree is a graph whose vertices are the leaves of and whose edges connect pairs of leaves whose distance in is at most . A graph is a leaf power if it is a -leaf power for some . Over 20 years ago, Nishimura et al. [J. Algorithms, 2002] asked if recognition of leaf powers was in P. Recently, Lafond [SODA 2022] showed an XP algorithm when parameterized by , while leaving the main question open. In this paper, we explore this question from the perspective of two alternative models of leaf powers, showing that both a linear and a star variant of leaf powers can be recognized in polynomial-time.
Cite
@article{arxiv.2105.12407,
title = {Recognition of Linear and Star Variants of Leaf Powers is in P},
author = {Benjamin Bergougnoux and Svein Høgemo and Jan Arne Telle and Martin Vatshelle},
journal= {arXiv preprint arXiv:2105.12407},
year = {2022}
}