{"id":"https://openalex.org/W1532852577","doi":"https://doi.org/10.46298/dmtcs.482","title":"On edge-intersection graphs of k-bend paths in grids","display_name":"On edge-intersection graphs of k-bend paths in grids","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W1532852577","doi":"https://doi.org/10.46298/dmtcs.482","mag":"1532852577"},"language":"en","primary_location":{"id":"doi:10.46298/dmtcs.482","is_oa":true,"landing_page_url":"https://doi.org/10.46298/dmtcs.482","pdf_url":"https://dmtcs.episciences.org/482/pdf","source":{"id":"https://openalex.org/S200334879","display_name":"Discrete Mathematics & Theoretical Computer Science","issn_l":"1365-8050","issn":["1365-8050","1462-7264"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4328141799","host_organization_name":"French association","host_organization_lineage":["https://openalex.org/P4328141799"],"host_organization_lineage_names":["French association"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics &amp; Theoretical Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://dmtcs.episciences.org/482/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038712987","display_name":"Th\u00e9r\u00e8se Biedl","orcid":"https://orcid.org/0000-0002-9003-3783"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Therese Biedl","raw_affiliation_strings":["David R. Cheriton School of Computer Science","David R. Cheriton School of Computer Science,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"David R. Cheriton School of Computer Science","institution_ids":[]},{"raw_affiliation_string":"David R. Cheriton School of Computer Science,","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037210315","display_name":"Michal Stern","orcid":"https://orcid.org/0000-0002-4073-635X"},"institutions":[{"id":"https://openalex.org/I4210087700","display_name":"Rothschild Caesarea Foundation","ror":"https://ror.org/0049whg19","country_code":"IL","type":"nonprofit","lineage":["https://openalex.org/I4210087700"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Michal Stern","raw_affiliation_strings":["Caesarea Rothschild Institute and Department of Computer Science"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Caesarea Rothschild Institute and Department of Computer Science","institution_ids":["https://openalex.org/I4210087700"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.3828,"has_fulltext":true,"cited_by_count":32,"citation_normalized_percentile":{"value":0.91779835,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"Vol. 12 no. 1","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7857224941253662},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7344363927841187},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.6657448410987854},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.6155871748924255},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.6110295653343201},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.5959973335266113},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.5579765439033508},{"id":"https://openalex.org/keywords/outerplanar-graph","display_name":"Outerplanar graph","score":0.5279029011726379},{"id":"https://openalex.org/keywords/longest-path-problem","display_name":"Longest path problem","score":0.47210589051246643},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45522934198379517},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.422479510307312},{"id":"https://openalex.org/keywords/clique-sum","display_name":"Clique-sum","score":0.41752058267593384},{"id":"https://openalex.org/keywords/lattice-graph","display_name":"Lattice graph","score":0.4157443642616272},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.4155910015106201},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3297822177410126},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.1484259068965912},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1351737380027771}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7857224941253662},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7344363927841187},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.6657448410987854},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.6155871748924255},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.6110295653343201},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.5959973335266113},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.5579765439033508},{"id":"https://openalex.org/C125792925","wikidata":"https://www.wikidata.org/wiki/Q3115604","display_name":"Outerplanar graph","level":5,"score":0.5279029011726379},{"id":"https://openalex.org/C1465435","wikidata":"https://www.wikidata.org/wiki/Q2916352","display_name":"Longest path problem","level":4,"score":0.47210589051246643},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45522934198379517},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.422479510307312},{"id":"https://openalex.org/C186942658","wikidata":"https://www.wikidata.org/wiki/Q5134410","display_name":"Clique-sum","level":5,"score":0.41752058267593384},{"id":"https://openalex.org/C145580432","wikidata":"https://www.wikidata.org/wiki/Q6497118","display_name":"Lattice graph","level":5,"score":0.4157443642616272},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.4155910015106201},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3297822177410126},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.1484259068965912},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1351737380027771}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.46298/dmtcs.482","is_oa":true,"landing_page_url":"https://doi.org/10.46298/dmtcs.482","pdf_url":"https://dmtcs.episciences.org/482/pdf","source":{"id":"https://openalex.org/S200334879","display_name":"Discrete Mathematics & Theoretical Computer Science","issn_l":"1365-8050","issn":["1365-8050","1462-7264"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4328141799","host_organization_name":"French association","host_organization_lineage":["https://openalex.org/P4328141799"],"host_organization_lineage_names":["French association"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics &amp; Theoretical Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00990425v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-00990425","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Discrete Mathematics and Theoretical Computer Science, 2010, Vol. 12 no. 1 (1), pp.1-12. &#x27E8;10.46298/dmtcs.482&#x27E9;","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:686fe8aa00a14d62a2ccab386d686cf0","is_oa":true,"landing_page_url":"https://doaj.org/article/686fe8aa00a14d62a2ccab386d686cf0","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Discrete Mathematics & Theoretical Computer Science, Vol Vol. 12 no. 1 (2010)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.46298/dmtcs.482","is_oa":true,"landing_page_url":"https://doi.org/10.46298/dmtcs.482","pdf_url":"https://dmtcs.episciences.org/482/pdf","source":{"id":"https://openalex.org/S200334879","display_name":"Discrete Mathematics & Theoretical Computer Science","issn_l":"1365-8050","issn":["1365-8050","1462-7264"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4328141799","host_organization_name":"French association","host_organization_lineage":["https://openalex.org/P4328141799"],"host_organization_lineage_names":["French association"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics &amp; Theoretical Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1532852577.pdf","grobid_xml":"https://content.openalex.org/works/W1532852577.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W140256473","https://openalex.org/W193938304","https://openalex.org/W1562280270","https://openalex.org/W1576090366","https://openalex.org/W1592330425","https://openalex.org/W1974970215","https://openalex.org/W1976489861","https://openalex.org/W1977240197","https://openalex.org/W2003525146","https://openalex.org/W2045870980","https://openalex.org/W2143474538","https://openalex.org/W2184935281","https://openalex.org/W2403103020","https://openalex.org/W6644554820"],"related_works":["https://openalex.org/W1976784955","https://openalex.org/W3101895193","https://openalex.org/W2133160845","https://openalex.org/W3217284998","https://openalex.org/W4308233685","https://openalex.org/W2031276298","https://openalex.org/W4225460864","https://openalex.org/W2950027724","https://openalex.org/W1979858320","https://openalex.org/W4298164694"],"abstract_inverted_index":{"Edge-intersection":[0],"graphs":[1,7,39,61,99,156,161],"of":[2,24,38,47,59,62,84,157],"paths":[3,16,31,48,63],"in":[4,17,44,49,64,86],"grids":[5],"are":[6,15],"that":[8,13,77,109,121],"can":[9,100,110],"be":[10,92,101,111],"represented":[11,112],"such":[12],"vertices":[14,23],"a":[18,33,65,126,135,146],"grid":[19,30,34,50],"and":[20,73,140,160],"edges":[21],"between":[22],"the":[25,57,82],"graph":[26,107,124,133,144],"exist":[27],"whenever":[28],"two":[29],"share":[32],"edge.":[35],"This":[36],"type":[37],"is":[40,89],"motivated":[41],"by":[42,70],"applications":[43],"conflict":[45],"resolution":[46],"networks.":[51],"In":[52],"this":[53],"paper,":[54],"we":[55,104],"continue":[56],"study":[58,105,153],"edge-intersection":[60],"grid,":[66],"which":[67],"was":[68],"initiated":[69],"Golumbic,":[71],"Lipshteyn":[72],"Stern.":[74],"We":[75,119,151],"show":[76,120],"for":[78,116],"any":[79],"k,":[80,95],"if":[81],"number":[83],"bends":[85],"each":[87],"path":[88],"restricted":[90],"to":[91],"at":[93],"most":[94],"then":[96],"not":[97],"all":[98],"represented.":[102],"Then":[103],"some":[106],"classes":[108],"with":[113,128,137,148,162],"k-bend":[114],"paths,":[115,130,139],"small":[117],"k.":[118],"every":[122,131,141],"planar":[123,142],"has":[125,134,145],"representation":[127,136,147],"5-bend":[129],"outerplanar":[132],"3-bend":[138],"bipartite":[143],"2-bend":[149],"paths.":[150],"also":[152],"line":[154],"graphs,":[155],"bounded":[158],"pathwidth,":[159],"-regular":[163],"edge":[164],"orientations.":[165]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
