2017
DOI: 10.1007/978-3-319-68705-6_21
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Algorithms for Outerplanar Graph Roots and Graph Roots of Pathwidth at Most 2

Abstract: Abstract. Deciding whether a given graph has a square root is a classical problem that has been studied extensively both from graph theoretic and from algorithmic perspectives. The problem is NP-complete in general, and consequently substantial effort has been dedicated to deciding whether a given graph has a square root that belongs to a particular graph class. There are both polynomial-time solvable and NP-complete cases, depending on the graph class. We contribute with new results in this direction. Given a… Show more

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Cited by 3 publications
(5 citation statements)
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“…Determining the complexity of H-SQUARE ROOT when H is the class of planar graphs is still a wide open problem. Golovach et al [12] also proved that squares of graphs of pathwidth at most 2 can be recognized in polynomial time. We recall that every cactus has treewidth at most 2.…”
Section: Discussionmentioning
confidence: 99%
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“…Determining the complexity of H-SQUARE ROOT when H is the class of planar graphs is still a wide open problem. Golovach et al [12] also proved that squares of graphs of pathwidth at most 2 can be recognized in polynomial time. We recall that every cactus has treewidth at most 2.…”
Section: Discussionmentioning
confidence: 99%
“…In fact, our algorithm can be modified to find a cactus root in the same time (if it exists). Every cactus is outerplanar, and recently Golovach et al [12] proved that squares of outerplanar graphs can be recognized in polynomial time. Determining the complexity of H-SQUARE ROOT when H is the class of planar graphs is still a wide open problem.…”
Section: Discussionmentioning
confidence: 99%
“…, B 4 . This implies that in order to prove condition (ii) it suffices to find a vertex v i that appears in at least five bags of B ∪ B 16 .…”
Section: Structural Lemmasmentioning
confidence: 99%
“…We may assume without loss of generality that B 1 = {x 1 , u, v 1 } and B 16 = {x 16 , u, v 2 }. Recall that v 1 does not belong to any bag B i for i ≥ 5 and x 16 belongs to B 16 , while u belongs to any bag between B 1 and B 16 . Then there exists a bag {v 1 , v 2 , u}, which has to be between B 1 = {x 1 , u, v 1 } and B 16 = {x 16 , u, v 2 }.…”
Section: Structural Lemmasmentioning
confidence: 99%
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