Squares of Low Clique Number

Abstract

Citation for published item:qolovhD etr nd urtshD hieter nd ulusmD hni¤ el nd tewrtD enthony @PHITA 9qures of low lique numerF9D iletroni notes in disrete mthemtisFD SS F ppF IWSEIWVF Further information on publisher's website: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractThe 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. By researching boundedness of the treewidth of a graph, we prove that Square Root is polynomial-time solvable on various graph classes of low clique number that are not minor-closed.

Finding Cactus Roots in Polynomial Time

“…This research was supported by EPSRC (EP/G043434/1), the Research Council of Norway (the project CLASSIS) and ANR project AGAPE. Extended abstracts containing results of this paper appeared in the proceedings of CTW 2016 [15] and IWOCA 2016 [13].…”

“…Extended abstracts containing results of this paper appeared in the proceedings of CTW 2016 [15] and IWOCA 2016 [13].…”

A linear kernel for finding square roots of almost planar graphs

“…They posed the complexity of Square Root restricted to split graphs and cographs as open problems. Recently, we proved that Square Root is linear-time solvable for 3-degenerate graphs and for (K r , P t )-free graphs for any two positive integers r and t [13].…”

Computing square roots of graphs with low maximum degree

“…graph class G complexity planar graphs [19] linear non-trivial and minor-closed [24] linear K4-free graphs [12] linear (Kr, Pt)-free graphs [12] linear 3-degenerate graphs [12] linear graphs of maximum degree ≤ 5 linear graphs of maximum degree ≤ 6 polynomial graphs of maximum average degree < 46 11 [11] polynomial line graphs [20] polynomial trivially perfect graphs [21] polynomial threshold graphs [21] polynomial chordal graphs [14] NP-complete Table 1: The known results for Square Root restricted to some special graph class G. Note that the row for planar graphs is absorbed by the row below. The two unreferenced results are the results of this paper.…”