Graph isomorphism completeness for chordal bipartite graphs and strongly chordal graphs

Uehara, Ryuhei; Toda, Seinosuke; Nagoya, Takayuki

doi:10.1016/j.dam.2004.06.008

Cited by 50 publications

(26 citation statements)

References 6 publications

(2 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Intuitively speaking, the linear (or one dimensional) structure of an interval graph makes these problems tractable, and this two dimensional extension makes them intractable. Such results for intractability also can be found in the literature; the Hamiltonian cycle problem is N P-complete on chordal bipartite graphs [37], and the graph isomorphism problem is GI-complete on chordal bipartite graphs and strongly chordal graphs [38].…”

Section: Introductionmentioning

confidence: 58%

Tractabilities and Intractabilities on Geometric Intersection Graphs

Uehara

2013

Algorithms

Self Cite

View full text Add to dashboard Cite

A graph is said to be an intersection graph if there is a set of objects such that each vertex corresponds to an object and two vertices are adjacent if and only if the corresponding objects have a nonempty intersection. There are several natural graph classes that have geometric intersection representations. The geometric representations sometimes help to prove tractability/intractability of problems on graph classes. In this paper, we show some results proved by using geometric representations.

show abstract

Section: Introductionmentioning

confidence: 58%

Tractabilities and Intractabilities on Geometric Intersection Graphs

Uehara

2013

Algorithms

Self Cite

View full text Add to dashboard Cite

show abstract

“…For each of these parameters, it remains an open question whether the problem is FPT. On the other hand, GI has been shown to be FPT when parameterized by eigenvalue multiplicity [5], tree distance width [21], the maximum size of a simplical component [19,20] and minimum feedback vertex set [12]. Bouland et al [2] showed that the problem is FPT when parameterized by the tree depth of a graph and extended this result to a parameter they termed generalised tree depth.…”

Section: Introductionmentioning

confidence: 94%

Graph Isomorphism Parameterized by Elimination Distance to Bounded Degree

Bulian

Dawar

2015

Algorithmica

View full text Add to dashboard Cite

A commonly studied means of parameterizing graph problems is the deletion distance from triviality (Guo et al., Parameterized and exact computation, Springer, Berlin, pp. 162-173, 2004), which counts vertices that need to be deleted from a graph to place it in some class for which efficient algorithms are known. In the context of graph isomorphism, we define triviality to mean a graph with maximum degree bounded by a constant, as such graph classes admit polynomial-time isomorphism tests. We generalise deletion distance to a measure we call elimination distance to triviality, based on elimination trees or tree-depth decompositions. We establish that graph canonisation, and thus graph isomorphism, is FPT when parameterized by elimination distance to bounded degree, extending results of Bouland et al. (Parameterized and exact computation, Springer, Berlin, pp. 218-230, 2012).

show abstract

“…In this sense, counting/random generation/enumeration on a graph class seems to be intractable if the isomorphism problem for the class is as hard as that for general graphs (See [38] for further details of this topic). It is known that the graph isomorphism problem can be solved in linear time for interval graphs [24].…”

Section: Resultsmentioning

confidence: 99%

Random Generation and Enumeration of Proper Interval Graphs

Saitoh

Yamanaka

Kiyomi

et al. 2010

IEICE Trans. Inf. & Syst.

Self Cite

View full text Add to dashboard Cite

SUMMARYWe investigate connected proper interval graphs without vertex labels. We first give the number of connected proper interval graphs of n vertices. Using this result, a simple algorithm that generates a connected proper interval graph uniformly at random up to isomorphism is presented. Finally an enumeration algorithm of connected proper interval graphs is proposed. The algorithm is based on reverse search, and it outputs each connected proper interval graph in O(1) time.

show abstract

Graph isomorphism completeness for chordal bipartite graphs and strongly chordal graphs

Cited by 50 publications

References 6 publications

Tractabilities and Intractabilities on Geometric Intersection Graphs

Tractabilities and Intractabilities on Geometric Intersection Graphs

Graph Isomorphism Parameterized by Elimination Distance to Bounded Degree

Random Generation and Enumeration of Proper Interval Graphs

Contact Info

Product

Resources

About