Squares of Low Maximum Degree
Data Structures and Algorithms
2016-08-30 v2 Discrete Mathematics
Combinatorics
Abstract
A graph H is a square root of a graph G if G can be obtained from H by adding an edge between any two vertices in H that are of distance 2. The Square Root problem is that of deciding whether a given graph admits a square root. This problem is only known to be NP-complete for chordal graphs and polynomial-time solvable for non-trivial minor-closed graph classes and a very limited number of other graph classes. We prove that Square Root is O(n)-time solvable for graphs of maximum degree 5 and O(n^4)-time solvable for graphs of maximum degree at most 6.
Cite
@article{arxiv.1608.06142,
title = {Squares of Low Maximum Degree},
author = {Manfred Cochefert and Jean-François Couturier and Petr A. Golovach and Dieter Kratsch and Daniël Paulusma and Anthony Stewart},
journal= {arXiv preprint arXiv:1608.06142},
year = {2016}
}