Induced Subgraph Isomorphism on proper interval and bipartite permutation graphs
Given two graphs G and H as input, the Induced Subgraph Isomorphism (ISI) problem is to decide whether G has an induced subgraph that is isomorphic to H. This problem is NP-complete already when G and H are restricted to disjoint unions of paths, and consequently also NP-complete on proper interval...
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| Veröffentlicht in: | Theoretical computer science 2015, Vol.562, p.252-269 |
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| creator | Heggernes, Pinar van 't Hof, Pim Meister, Daniel Villanger, Yngve |
| description | Given two graphs G and H as input, the Induced Subgraph Isomorphism (ISI) problem is to decide whether G has an induced subgraph that is isomorphic to H. This problem is NP-complete already when G and H are restricted to disjoint unions of paths, and consequently also NP-complete on proper interval graphs and on bipartite permutation graphs. We show that ISI can be solved in polynomial time on proper interval graphs and on bipartite permutation graphs, provided that H is connected. As a consequence, we obtain that ISI is fixed-parameter tractable on these two graph classes, when parametrised by the number of connected components of H. Our results contrast and complement the following known results: W[1]-hardness of ISI on interval graphs when parametrised by the number of vertices of H, NP-completeness of ISI on connected interval graphs and on connected permutation graphs, and NP-completeness of Subgraph Isomorphism on connected proper interval graphs and connected bipartite permutation graphs. |
| doi_str_mv | 10.1016/j.tcs.2014.10.002 |
| format | Article |
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This problem is NP-complete already when G and H are restricted to disjoint unions of paths, and consequently also NP-complete on proper interval graphs and on bipartite permutation graphs. We show that ISI can be solved in polynomial time on proper interval graphs and on bipartite permutation graphs, provided that H is connected. As a consequence, we obtain that ISI is fixed-parameter tractable on these two graph classes, when parametrised by the number of connected components of H. Our results contrast and complement the following known results: W[1]-hardness of ISI on interval graphs when parametrised by the number of vertices of H, NP-completeness of ISI on connected interval graphs and on connected permutation graphs, and NP-completeness of Subgraph Isomorphism on connected proper interval graphs and connected bipartite permutation graphs.</description><identifier>ISSN: 0304-3975</identifier><identifier>EISSN: 1879-2294</identifier><identifier>DOI: 10.1016/j.tcs.2014.10.002</identifier><language>eng</language><publisher>Elsevier B.V</publisher><subject>Complement ; Fixed-parameter tractable ; Graph theory ; Graphs ; Induced subgraphs ; Intervals ; Isomorphism ; Permutations ; Polynomial-time ; Polynomials ; Unions</subject><ispartof>Theoretical computer science, 2015, Vol.562, p.252-269</ispartof><rights>2014 Elsevier B.V.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c396t-7b0e91100cbe2c6b5735160ebd45b2f57236f8c039aceaa748bb840d76899a2d3</citedby><cites>FETCH-LOGICAL-c396t-7b0e91100cbe2c6b5735160ebd45b2f57236f8c039aceaa748bb840d76899a2d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.tcs.2014.10.002$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,3550,4024,27923,27924,27925,45995</link.rule.ids></links><search><creatorcontrib>Heggernes, Pinar</creatorcontrib><creatorcontrib>van 't Hof, Pim</creatorcontrib><creatorcontrib>Meister, Daniel</creatorcontrib><creatorcontrib>Villanger, Yngve</creatorcontrib><title>Induced Subgraph Isomorphism on proper interval and bipartite permutation graphs</title><title>Theoretical computer science</title><description>Given two graphs G and H as input, the Induced Subgraph Isomorphism (ISI) problem is to decide whether G has an induced subgraph that is isomorphic to H. 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Our results contrast and complement the following known results: W[1]-hardness of ISI on interval graphs when parametrised by the number of vertices of H, NP-completeness of ISI on connected interval graphs and on connected permutation graphs, and NP-completeness of Subgraph Isomorphism on connected proper interval graphs and connected bipartite permutation graphs.</description><subject>Complement</subject><subject>Fixed-parameter tractable</subject><subject>Graph theory</subject><subject>Graphs</subject><subject>Induced subgraphs</subject><subject>Intervals</subject><subject>Isomorphism</subject><subject>Permutations</subject><subject>Polynomial-time</subject><subject>Polynomials</subject><subject>Unions</subject><issn>0304-3975</issn><issn>1879-2294</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNp9kE1PwzAMhiMEEmPwA7j1yKXFSdukESc08TFpEkjAOUpSj2VaP0jSSfx7MsYZXyzb72vZDyHXFAoKlN9ui2hDwYBWqS4A2AmZ0UbInDFZnZIZlFDlpRT1ObkIYQspasFn5HXZt5PFNnubzKfX4yZbhqEb_LhxocuGPhv9MKLPXB_R7_Uu032bGTdqH13ELI26KerokvLXHi7J2VrvAl795Tn5eHx4Xzznq5en5eJ-ldtS8pgLAygpBbAGmeWmFmVNOaBpq9qwdS1YydeNhVJqi1qLqjGmqaAVvJFSs7ack5vj3nTg14Qhqs4Fi7ud7nGYgqKcAwgmOSQpPUqtH0LwuFajd53234qCOtBTW5XoqQO9QyvRS567owfTD3uHXgXrsE-knEcbVTu4f9w_oVx4sQ</recordid><startdate>2015</startdate><enddate>2015</enddate><creator>Heggernes, Pinar</creator><creator>van 't Hof, Pim</creator><creator>Meister, Daniel</creator><creator>Villanger, Yngve</creator><general>Elsevier B.V</general><scope>6I.</scope><scope>AAFTH</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>2015</creationdate><title>Induced Subgraph Isomorphism on proper interval and bipartite permutation graphs</title><author>Heggernes, Pinar ; van 't Hof, Pim ; Meister, Daniel ; Villanger, Yngve</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c396t-7b0e91100cbe2c6b5735160ebd45b2f57236f8c039aceaa748bb840d76899a2d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Complement</topic><topic>Fixed-parameter tractable</topic><topic>Graph theory</topic><topic>Graphs</topic><topic>Induced subgraphs</topic><topic>Intervals</topic><topic>Isomorphism</topic><topic>Permutations</topic><topic>Polynomial-time</topic><topic>Polynomials</topic><topic>Unions</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Heggernes, Pinar</creatorcontrib><creatorcontrib>van 't Hof, Pim</creatorcontrib><creatorcontrib>Meister, Daniel</creatorcontrib><creatorcontrib>Villanger, Yngve</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Theoretical computer science</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Heggernes, Pinar</au><au>van 't Hof, Pim</au><au>Meister, Daniel</au><au>Villanger, Yngve</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Induced Subgraph Isomorphism on proper interval and bipartite permutation graphs</atitle><jtitle>Theoretical computer science</jtitle><date>2015</date><risdate>2015</risdate><volume>562</volume><spage>252</spage><epage>269</epage><pages>252-269</pages><issn>0304-3975</issn><eissn>1879-2294</eissn><abstract>Given two graphs G and H as input, the Induced Subgraph Isomorphism (ISI) problem is to decide whether G has an induced subgraph that is isomorphic to H. 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| source | Elsevier ScienceDirect Journals Complete; EZB-FREE-00999 freely available EZB journals |
| subjects | Complement Fixed-parameter tractable Graph theory Graphs Induced subgraphs Intervals Isomorphism Permutations Polynomial-time Polynomials Unions |
| title | Induced Subgraph Isomorphism on proper interval and bipartite permutation graphs |
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