A Linear Recognition Algorithm for Cographs

Corneil, Derek G.; Perl, Yehoshua; Stewart, Lorna

doi:10.1137/0214065

Cited by 560 publications

(352 citation statements)

References 8 publications

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“…Moreover, given a graph G, we can determine in linear time whether G is a cograph and, if this is not the case, return an induced P 4 [8,12]. This implies that in O(k · (m + n)) time, with k being the distance to cographs, we can compute a set K ⊆ V of size at most 4k such that G − K is a cograph.…”

Section: Parameters Incomparable With Degeneracymentioning

confidence: 99%

“…To this end, we need the following notation. Every cograph has a binary cotree representation which can be computed in linear time [12]. A cotree is a rooted tree in which each leaf corresponds to a vertex in the cograph and each inner node either represents a disjoint union or a join of its children.…”

Section: Distance To Bipartite Graphs Chordal Graphs or Cographmentioning

confidence: 99%

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Parameterized Aspects of Triangle Enumeration

Bentert

Fluschnik

Nichterlein

et al. 2017

Fundamentals of Computation Theory

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Listing all triangles in an undirected graph is a fundamental graph primitive with numerous applications. It is trivially solvable in time cubic in the number of vertices. It has seen a significant body of work contributing to both theoretical aspects (e.g., lower and upper bounds on running time, adaption to new computational models) as well as practical aspects (e.g. algorithms tuned for large graphs). Motivated by the fact that the worst-case running time is cubic, we perform a systematic parameterized complexity study of triangle enumeration, providing both positive results (new enumerative kernelizations, "subcubic" parameterized solving algorithms) as well as negative results (likely uselessness in terms of "faster" parameterized algorithms of certain parameters such as graph diameter).

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Section: Parameters Incomparable With Degeneracymentioning

confidence: 99%

Section: Distance To Bipartite Graphs Chordal Graphs or Cographmentioning

confidence: 99%

Parameterized Aspects of Triangle Enumeration

Bentert

Fluschnik

Nichterlein

et al. 2017

Fundamentals of Computation Theory

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“…Corneil, Perl and Stewart [10] proved that the problem of deciding whether a graph with n vertices and m edges is a cograph can be solved in time O(n + m). They also showed that in the same time it is possible to construct its cotree (if it exists).…”

Section: Cographsmentioning

confidence: 99%

Contraction Blockers for Graphs with Forbidden Induced Paths

Diner

Paulusma

Picouleau

et al. 2015

Lecture Notes in Computer Science

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hinerD ¤ yF nd ulusm D hF nd i oule uD gF nd iesD fF @PHISA 9gontr tion lo kers for gr phs with for idden indu ed p thsF9D in elgorithms nd omplexity X Wth sntern tion l gonferen eD gseg PHISD risD pr n eD w y PHEPPD PHIS Y pro eedingsF D ppF IWREPHUF ve ture notes in omputer s ien eF @WHUWAF Further information on publisher's website:Publisher's copyright statement:The nal publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-18173-814.Additional information: 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-pro t 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. Abstract. We consider the following problem: can a certain graph parameter of some given graph be reduced by at least d for some integer d via at most k edge contractions for some given integer k? We examine three graph parameters: the chromatic number, clique number and independence number. For each of these graph parameters we show that, when d is part of the input, this problem is polynomial-time solvable on P4-free graphs and NP-complete as well as W[1]-hard, with parameter d, for split graphs. As split graphs form a subclass of P5-free graphs, both results together give a complete complexity classification for Pfree graphs. The W[1]-hardness result implies that it is unlikely that the problem is fixed-parameter tractable for split graphs with parameter d. But we do show, on the positive side, that the problem is polynomialtime solvable, for each parameter, on split graphs if d is fixed, i.e., not part of the input. We also initiate a study into other subclasses of perfect graphs, namely cobipartite graphs and interval graphs.

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“…Finally we present our main algorithmic result: an algorithm that solves computation problem, namely the problem of computing a minimal cograph completion of an arbitrary input graph. This algorithm can be viewed as a generalization of the cograph recognition algorithm given in [14], due to its incremental nature. We consider, in fact, the input graph one vertex at the time, and we complete it locally in an on-line fashion.…”

Section: Introductionmentioning

confidence: 99%

Characterizing and Computing Minimal Cograph Completions

Lokshtanov

Mancini

Papadopoulos

Frontiers in Algorithmics

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A cograph completion of an arbitrary graph G is a cograph supergraph of G on the same vertex set. Such a completion is called minimal if the set of edges added to G is inclusion minimal. In this paper we present two results on minimal cograph completions. The first is a a characterization that allows us to check in linear time whether a given cograph completion is minimal. The second result is a vertex incremental algorithm to compute a minimal cograph completion H of an arbitrary input graph G in O(|V (H)| + |E(H)|) time.

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A Linear Recognition Algorithm for Cographs

Cited by 560 publications

References 8 publications

Parameterized Aspects of Triangle Enumeration

Parameterized Aspects of Triangle Enumeration

Contraction Blockers for Graphs with Forbidden Induced Paths

Characterizing and Computing Minimal Cograph Completions

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