Parameterized algorithms for recognizing monopolar and 2-subcolorable graphs

Iyad Kanj; Christian Komusiewicz; Manuel Sorge; Erik Jan van Leeuwen

doi:10.1016/j.jcss.2017.08.002

Parameterized algorithms for recognizing monopolar and 2-subcolorable graphs

Iyad Kanj
, Christian Komusiewicz
, Manuel Sorge
, Erik Jan van Leeuwen

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

A graph G is a (Π_A,Π_B)-graph if V(G) can be bipartitioned into A and B such that G[A] satisfies property Π_A and G[B] satisfies property Π_B. The (Π_A,Π_B)-RECOGNITION problem is to recognize whether a given graph is a (Π_A,Π_B)-graph. There are many (Π_A,Π_B)-RECOGNITION problems, including the recognition problems for bipartite, split, and unipolar graphs. We present efficient algorithms for many cases of (Π_A,Π_B)-RECOGNITION based on a technique which we dub inductive recognition. In particular, we give fixed-parameter algorithms for two NP-hard (Π_A,Π_B)-RECOGNITION problems, MONOPOLAR RECOGNITION and 2-SUBCOLORING, parameterized by the number of maximal cliques in G[A]. We complement our algorithmic results with several hardness results for (Π_A,Π_B)-RECOGNITION.

Original language	English
Pages (from-to)	22-47
Number of pages	26
Journal	Journal of Computer and System Sciences
Volume	92
DOIs	https://doi.org/10.1016/j.jcss.2017.08.002
State	Published - 1 Mar 2018
Externally published	Yes

Keywords

Fixed-parameter algorithms
Graph classes
Monopolar graphs
Split graphs
Subcolorings
Unipolar graphs
Vertex-partition problems

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science
Computer Networks and Communications
Computational Theory and Mathematics
Applied Mathematics

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10.1016/j.jcss.2017.08.002

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@article{86fa661b4bb64e2c8d71bc9a9c359923,

title = "Parameterized algorithms for recognizing monopolar and 2-subcolorable graphs",

abstract = "A graph G is a (ΠA,ΠB)-graph if V(G) can be bipartitioned into A and B such that G[A] satisfies property ΠA and G[B] satisfies property ΠB. The (ΠA,ΠB)-RECOGNITION problem is to recognize whether a given graph is a (ΠA,ΠB)-graph. There are many (ΠA,ΠB)-RECOGNITION problems, including the recognition problems for bipartite, split, and unipolar graphs. We present efficient algorithms for many cases of (ΠA,ΠB)-RECOGNITION based on a technique which we dub inductive recognition. In particular, we give fixed-parameter algorithms for two NP-hard (ΠA,ΠB)-RECOGNITION problems, MONOPOLAR RECOGNITION and 2-SUBCOLORING, parameterized by the number of maximal cliques in G[A]. We complement our algorithmic results with several hardness results for (ΠA,ΠB)-RECOGNITION.",

keywords = "Fixed-parameter algorithms, Graph classes, Monopolar graphs, Split graphs, Subcolorings, Unipolar graphs, Vertex-partition problems",

author = "Iyad Kanj and Christian Komusiewicz and Manuel Sorge and \{van Leeuwen\}, \{Erik Jan\}",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

year = "2018",

month = mar,

day = "1",

doi = "10.1016/j.jcss.2017.08.002",

language = "English",

volume = "92",

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journal = "Journal of Computer and System Sciences",

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TY - JOUR

T1 - Parameterized algorithms for recognizing monopolar and 2-subcolorable graphs

AU - Kanj, Iyad

AU - Komusiewicz, Christian

AU - Sorge, Manuel

AU - van Leeuwen, Erik Jan

PY - 2018/3/1

Y1 - 2018/3/1

N2 - A graph G is a (ΠA,ΠB)-graph if V(G) can be bipartitioned into A and B such that G[A] satisfies property ΠA and G[B] satisfies property ΠB. The (ΠA,ΠB)-RECOGNITION problem is to recognize whether a given graph is a (ΠA,ΠB)-graph. There are many (ΠA,ΠB)-RECOGNITION problems, including the recognition problems for bipartite, split, and unipolar graphs. We present efficient algorithms for many cases of (ΠA,ΠB)-RECOGNITION based on a technique which we dub inductive recognition. In particular, we give fixed-parameter algorithms for two NP-hard (ΠA,ΠB)-RECOGNITION problems, MONOPOLAR RECOGNITION and 2-SUBCOLORING, parameterized by the number of maximal cliques in G[A]. We complement our algorithmic results with several hardness results for (ΠA,ΠB)-RECOGNITION.

AB - A graph G is a (ΠA,ΠB)-graph if V(G) can be bipartitioned into A and B such that G[A] satisfies property ΠA and G[B] satisfies property ΠB. The (ΠA,ΠB)-RECOGNITION problem is to recognize whether a given graph is a (ΠA,ΠB)-graph. There are many (ΠA,ΠB)-RECOGNITION problems, including the recognition problems for bipartite, split, and unipolar graphs. We present efficient algorithms for many cases of (ΠA,ΠB)-RECOGNITION based on a technique which we dub inductive recognition. In particular, we give fixed-parameter algorithms for two NP-hard (ΠA,ΠB)-RECOGNITION problems, MONOPOLAR RECOGNITION and 2-SUBCOLORING, parameterized by the number of maximal cliques in G[A]. We complement our algorithmic results with several hardness results for (ΠA,ΠB)-RECOGNITION.

KW - Fixed-parameter algorithms

KW - Graph classes

KW - Monopolar graphs

KW - Split graphs

KW - Subcolorings

KW - Unipolar graphs

KW - Vertex-partition problems

UR - https://www.scopus.com/pages/publications/85028692116

U2 - 10.1016/j.jcss.2017.08.002

DO - 10.1016/j.jcss.2017.08.002

M3 - Article

AN - SCOPUS:85028692116

SN - 0022-0000

VL - 92

SP - 22

EP - 47

JO - Journal of Computer and System Sciences

JF - Journal of Computer and System Sciences

ER -

Parameterized algorithms for recognizing monopolar and 2-subcolorable graphs

Abstract

Keywords

ASJC Scopus subject areas

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