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arXiv · 1608.06142

Squares of Low Maximum Degree

Manfred Cochefert·Jean-François Couturier·Petr A. Golovach·Dieter Kratsch·Daniël Paulusma·Anthony Stewart
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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.

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Manfred Cochefert, Jean-François Couturier, Petr A. Golovach, Dieter Kratsch, Daniël Paulusma, Anthony Stewart. 2016-08-22. Squares of Low Maximum Degree. https://arxiv.org/abs/1608.06142

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