{"id":"https://openalex.org/W4323651098","doi":"https://doi.org/10.1016/j.dam.2026.01.017","title":"Cops and robbers on multi-layer graphs","display_name":"Cops and robbers on multi-layer graphs","publication_year":2026,"publication_date":"2026-01-28","ids":{"openalex":"https://openalex.org/W4323651098","doi":"https://doi.org/10.1016/j.dam.2026.01.017"},"language":"en","primary_location":{"id":"doi:10.1016/j.dam.2026.01.017","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.dam.2026.01.017","pdf_url":null,"source":{"id":"https://openalex.org/S171741597","display_name":"Discrete Applied Mathematics","issn_l":"0166-218X","issn":["0166-218X","1872-6771"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"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 Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.dam.2026.01.017","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014039487","display_name":"Jessica Enright","orcid":"https://orcid.org/0000-0002-0266-3292"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jessica Enright","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088807601","display_name":"Kitty Meeks","orcid":"https://orcid.org/0000-0001-5299-3073"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kitty Meeks","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014747179","display_name":"William Pettersson","orcid":"https://orcid.org/0000-0003-0040-2088"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"William Pettersson","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5067885700","display_name":"John Sylvester","orcid":"https://orcid.org/0000-0002-6543-2934"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"John Sylvester","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-6543-2934","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2750,"currency":"USD","value_usd":2750},"apc_paid":{"value":2750,"currency":"USD","value_usd":2750},"fwci":8.6845,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.94130219,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"385","issue":null,"first_page":"109","last_page":"133"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9980999827384949,"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":0.9980999827384949,"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/T11031","display_name":"Game Theory and Applications","score":0.9873999953269958,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9729999899864197,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/treewidth","display_name":"Treewidth","score":0.73501056432724},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6615033745765686},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6593091487884521},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6308781504631042},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.5348979234695435},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.5262700319290161},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.4951607286930084},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44992223381996155},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.44469499588012695},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.4341456890106201},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.42704808712005615},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.24051234126091003}],"concepts":[{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.73501056432724},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6615033745765686},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6593091487884521},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6308781504631042},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.5348979234695435},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.5262700319290161},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.4951607286930084},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44992223381996155},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.44469499588012695},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4341456890106201},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.42704808712005615},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.24051234126091003},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1016/j.dam.2026.01.017","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.dam.2026.01.017","pdf_url":null,"source":{"id":"https://openalex.org/S171741597","display_name":"Discrete Applied Mathematics","issn_l":"0166-218X","issn":["0166-218X","1872-6771"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"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 Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2303.03962","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2303.03962","pdf_url":"https://arxiv.org/pdf/2303.03962","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:eprints.gla.ac.uk:377433","is_oa":true,"landing_page_url":"https://eprints.gla.ac.uk/view/author/28436.html>","pdf_url":"https://eprints.gla.ac.uk/377433/2/377433.pdf","source":{"id":"https://openalex.org/S4210235606","display_name":"ENLIGHTEN (Jurnal Bimbingan dan Konseling Islam)","issn_l":"2622-8912","issn":["2622-8912","2622-8920"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Articles"},{"id":"pmh:doi:10.48550/arxiv.2303.03962","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:eprints.gla.ac.uk:304469","is_oa":false,"landing_page_url":"https://eprints.gla.ac.uk/304469/","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"NonPeerReviewed"},{"id":"doi:10.48550/arxiv.2303.03962","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2303.03962","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1016/j.dam.2026.01.017","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.dam.2026.01.017","pdf_url":null,"source":{"id":"https://openalex.org/S171741597","display_name":"Discrete Applied Mathematics","issn_l":"0166-218X","issn":["0166-218X","1872-6771"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"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 Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7200000286102295,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G7222129398","display_name":"Multilayer Algorithmics to Leverage Graph Structure (MultilayerALGS)","funder_award_id":"EP/T004878/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320320337","display_name":"University of Glasgow","ror":"https://ror.org/00vtgdb53"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W2046635105","https://openalex.org/W1998076608","https://openalex.org/W1996456693","https://openalex.org/W4410321350","https://openalex.org/W2055205054","https://openalex.org/W3205354433","https://openalex.org/W3026493967","https://openalex.org/W2343286580","https://openalex.org/W4240838206","https://openalex.org/W4206792021","https://openalex.org/W4393282085","https://openalex.org/W2580476827","https://openalex.org/W2015309545","https://openalex.org/W1833292044","https://openalex.org/W3004777475","https://openalex.org/W1986861105","https://openalex.org/W2018047324","https://openalex.org/W2952565476","https://openalex.org/W2072757898","https://openalex.org/W3037826211","https://openalex.org/W1974452921","https://openalex.org/W3181621922","https://openalex.org/W1537525952","https://openalex.org/W2028400828","https://openalex.org/W4281928119","https://openalex.org/W2036303537","https://openalex.org/W2054375402","https://openalex.org/W2011911122","https://openalex.org/W2172190736","https://openalex.org/W2963041295"],"related_works":["https://openalex.org/W1480846237","https://openalex.org/W2029854525","https://openalex.org/W2012687409","https://openalex.org/W1548014395","https://openalex.org/W3037533092","https://openalex.org/W143512583","https://openalex.org/W2889180046","https://openalex.org/W1511821218","https://openalex.org/W1976463682","https://openalex.org/W1544821268"],"abstract_inverted_index":{"We":[0,27,71],"generalise":[1],"the":[2,15,33,48,64,68,86,117,144,204,231,236],"popular":[3],"cops":[4,38,81,113,148],"and":[5,14,45,96,169,180,202],"robbers":[6],"game":[7],"to":[8,19,36,39,77,84,109,150,190],"multi-layer":[9,49,156,197,213],"graphs,":[10,179],"where":[11,158,228],"each":[12,159],"cop":[13,50,65,91,214],"robber":[16,118,153],"are":[17,82,172],"restricted":[18],"a":[20,94,97,105,121,126,132,138,152,196,221],"single":[21],"layer":[22,92,119,168],"(or":[23],"set":[24,98],"of":[25,63,67,99,128,131,147,161,182,199,206,210,233],"edges).":[26],"show":[28,203],"that":[29,47,73],"initial":[30],"intuition":[31],"about":[32],"best":[34],"way":[35],"allocate":[37],"layers":[40,171],"is":[41,52,75,93,120,143,163,216,230],"not":[42],"always":[43],"correct,":[44],"prove":[46],"number":[51,146,215,232],"neither":[53],"bounded":[54,183,217],"from":[55,218],"above":[56],"nor":[57],"below":[58,219],"by":[59,220],"any":[60],"increasing":[61],"function":[62],"numbers":[66],"individual":[69],"layers.":[70],"determine":[72,110,186],"it":[74],"NP-hard":[76],"decide":[78],"if":[79,89,111],"$k$":[80,112],"sufficient":[83],"catch":[85,151],"robber,":[87],"even":[88],"every":[90],"tree":[95],"isolated":[100],"vertices.":[101],"However,":[102],"we":[103,124,185,194],"give":[104],"polynomial":[106],"time":[107],"algorithm":[108],"can":[114],"win":[115],"when":[116],"tree.":[122],"Additionally,":[123],"investigate":[125],"question":[127],"worst-case":[129],"divisions":[130],"simple":[133,139],"graph":[134,140],"into":[135],"layers:":[136],"given":[137],"$G$,":[141],"what":[142],"maximum":[145],"required":[149],"over":[154],"all":[155,170],"graphs":[157,181,211],"edge":[160],"$G$":[162],"in":[164,235],"at":[165],"least":[166],"one":[167],"connected?":[173],"For":[174],"cliques,":[175],"suitably":[176],"dense":[177],"random":[178],"treewidth,":[184],"this":[187],"parameter":[188],"up":[189],"multiplicative":[191],"constants.":[192],"Lastly":[193],"consider":[195],"variant":[198],"Meyniel's":[200],"conjecture,":[201],"existence":[205],"an":[207],"infinite":[208],"family":[209],"whose":[212],"constant":[222],"times":[223],"$n":[224],"/":[225],"\\log":[226],"n$,":[227],"$n$":[229],"vertices":[234],"graph.":[237]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-18T07:39:51.176621","created_date":"2023-03-10T00:00:00"}
