Helly Circular-Arc Graph Isomorphism Is in Logspace

Köbler, Johannes; Kuhnert, Sebastian; Verbitsky, Oleg

doi:10.1007/978-3-642-40313-2_56

Cited by 8 publications

(25 citation statements)

References 14 publications

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“…The concept of flip sets has already been implicitly defined and used in both [14] and [10]. They observed that λ (X) is an interval matrix whenever X is a flip set of a CA matrix λ.…”

Section: Flip Trickmentioning

confidence: 99%

“…This means the arc ρ(v) does not contain the point x for every vertex v ∈ V (λ). Consider the cs di cc cd ov Z 10 cd cc di cs ov Z 11 di cs cd cc ov representation ρ (X) ∈ N ((λ (X) ) (X) ) = N (λ). Then it can be checked that ρ (X) (v) contains the point x iff v is in X and therefore X is a flip set with respect to λ.…”

Section: Flip Trickmentioning

confidence: 99%

“…We conclude this section by restating the invariant flip set function that was used in [10] to compute canonical representations for Helly CA graphs and explain why it is correct:…”

Section: Flip Trickmentioning

confidence: 99%

“…In this article we explain how the method used in [10] to obtain canonical representation for Helly CA graphs can be adapted to CA graphs in general. Following this approach, canonical representations for CA graphs can be found by computing certain subsets of vertices called flip sets in an isomorphism-invariant manner.…”

Section: Introductionmentioning

confidence: 99%

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Canonical Representations for Circular-Arc Graphs Using Flip Sets

Chandoo

2018

Algorithmica

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We show that computing canonical representations for circular-arc (CA) graphs reduces to computing certain subsets of vertices called flip sets. For a broad class of CA graphs, which we call uniform, it suffices to compute a CA representation to find such flip sets. As a consequence canonical representations for uniform CA graphs can be obtained in polynomial-time. We then investigate what kind of CA graphs pose a challenge to this approach. This leads us to introduce the notion of restricted CA matrices and show that the canonical representation problem for CA graphs is logspace-reducible to that of restricted CA matrices. As a byproduct, we obtain the result that CA graphs without induced 4-cycles can be canonized in logspace.

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“…The concept of flip sets has already been implicitly defined and used in both [14] and [10]. They observed that λ (X) is an interval matrix whenever X is a flip set of a CA matrix λ.…”

Section: Flip Trickmentioning

confidence: 99%

Section: Flip Trickmentioning

confidence: 99%

“…We conclude this section by restating the invariant flip set function that was used in [10] to compute canonical representations for Helly CA graphs and explain why it is correct:…”

Section: Flip Trickmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Canonical Representations for Circular-Arc Graphs Using Flip Sets

Chandoo

2018

Algorithmica

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“…In [12] we already presented a logspace canonical representation algorithm for HCA graphs. Our approach in [12] uses techniques developed by McConnell in [15], and the algorithm is rather intricate. Now we suggest an alternative approach that is independent of [15].…”

Section: Introductionmentioning

confidence: 99%

On the isomorphism problem for Helly circular-arc graphs

Köbler

Kuhnert

Verbitsky

2016

Information and Computation

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The isomorphism problem is known to be efficiently solvable for interval graphs, while for the larger class of circular-arc graphs its complexity status stays open. We consider the intermediate class of intersection graphs for families of circular arcs that satisfy the Helly property. We solve the isomorphism problem for this class in logarithmic space. If an input graph has a Helly circular-arc model, our algorithm constructs it canonically, which means that the models constructed for isomorphic graphs are equal.

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