{"id":"https://openalex.org/W7207550749","doi":"https://doi.org/10.48550/arxiv.2609.01745","title":"The directional localization game on graphs","display_name":"The directional localization game on graphs","publication_year":2026,"publication_date":"2026-09-01","ids":{"openalex":"https://openalex.org/W7207550749","doi":"https://doi.org/10.48550/arxiv.2609.01745"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.01745","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01745","pdf_url":"https://arxiv.org/pdf/2609.01745","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.01745","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5119820710","display_name":"John Jones","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jones, John","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5071805417","display_name":"William B. Kinnersley","orcid":"https://orcid.org/0000-0003-3849-4221","observed_orcids":["https://orcid.org/0000-0003-3849-4221"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kinnersley, William B.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"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":0.9369999766349792,"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":0.9369999766349792,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.04910000041127205,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.0027000000700354576,"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/graph-search","display_name":"graph search","score":0.6890000104904175},{"id":"https://openalex.org/keywords/cop-number","display_name":"cop number","score":0.421999990940094},{"id":"https://openalex.org/keywords/shortest-path","display_name":"shortest path","score":0.6309999823570251},{"id":"https://openalex.org/keywords/chordal-graphs","display_name":"chordal graphs","score":0.8130000233650208},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.9570000171661377},{"id":"https://openalex.org/keywords/degeneracy","display_name":"degeneracy","score":0.9570000171661377},{"id":"https://openalex.org/keywords/treewidth","display_name":"treewidth","score":1.0}],"concepts":[{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5838000178337097},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.5777000188827515},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5609999895095825},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5593000054359436},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.48750001192092896},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.40779998898506165},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4066999852657318},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.39419999718666077},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.38440001010894775},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.36730000376701355},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.362199991941452},{"id":"https://openalex.org/C38754835","wikidata":"https://www.wikidata.org/wiki/Q2003238","display_name":"Strongly connected component","level":2,"score":0.33730000257492065},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.32820001244544983},{"id":"https://openalex.org/C95815963","wikidata":"https://www.wikidata.org/wiki/Q1377033","display_name":"Game tree","level":4,"score":0.3271999955177307},{"id":"https://openalex.org/C69919132","wikidata":"https://www.wikidata.org/wiki/Q1144819","display_name":"Polyomino","level":3,"score":0.31619998812675476},{"id":"https://openalex.org/C167573328","wikidata":"https://www.wikidata.org/wiki/Q7439054","display_name":"Screening game","level":4,"score":0.30320000648498535},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3027999997138977},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.299699991941452},{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.2937999963760376},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2922999858856201},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.26930001378059387},{"id":"https://openalex.org/C43413943","wikidata":"https://www.wikidata.org/wiki/Q4927193","display_name":"Block graph","level":5,"score":0.26820001006126404},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.259799987077713}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.01745","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01745","pdf_url":"https://arxiv.org/pdf/2609.01745","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.01745","doi":"https://doi.org/10.48550/arxiv.2609.01745","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.01745","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.01745","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01745","pdf_url":"https://arxiv.org/pdf/2609.01745","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7207550749.pdf","grobid_xml":"https://content.openalex.org/works/W7207550749.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4292214272","https://openalex.org/W4380928971","https://openalex.org/W3131033879","https://openalex.org/W2754536942","https://openalex.org/W2808050500","https://openalex.org/W3161320300","https://openalex.org/W2981873291","https://openalex.org/W3046516391","https://openalex.org/W6979284725","https://openalex.org/W3139123665"],"abstract_inverted_index":{"In":[0,48,60],"the":[1,26,28,31,35,45,56,72,78,98,114,122,145,156,159],"localization":[2,58,116,124,147],"game":[3,110,125],"on":[4,18,91,111,126],"a":[5,8,53,75,92,150],"graph":[6,151],"$G$,":[7],"team":[9],"of":[10,64,87,104,118,129,139,149,155,161],"cops":[11,27,38,73,105],"searches":[12],"for":[13],"an":[14],"invisible,":[15],"mobile":[16],"robber":[17,79],"$G$":[19,112,152],"by":[20],"\"probing\"":[21],"vertices;":[22],"each":[23],"probe":[24,74],"tells":[25],"distance":[29],"from":[30,95],"probed":[32],"vertex":[33,76],"to":[34,97,107],"robber.":[36],"The":[37,101],"win":[39,108],"if":[40],"they":[41,68],"can":[42],"uniquely":[43],"determine":[44],"robber's":[46,99],"location.":[47,100],"this":[49,61,109],"paper,":[50],"we":[51],"introduce":[52],"related":[54],"game:":[55],"directional":[57,115,123,146],"game.":[59],"game,":[62],"instead":[63],"probes":[65],"returning":[66],"distances,":[67],"return":[69],"directions:":[70],"when":[71],"$v$,":[77],"must":[80],"respond":[81],"with":[82],"one":[83],"or":[84],"more":[85],"neighbors":[86],"$v$":[88,96],"that":[89],"lie":[90],"shortest":[93],"path":[94],"minimum":[102],"number":[103,117,148],"needed":[106],"is":[113],"$G$.":[119,162],"We":[120,142],"study":[121],"several":[127],"classes":[128],"graphs,":[130,133],"including":[131],"chordal":[132],"Cartesian":[134],"products,":[135],"and":[136,158],"incidence":[137],"graphs":[138],"projective":[140],"planes.":[141],"also":[143],"bound":[144],"in":[153],"terms":[154],"degeneracy":[157],"treewidth":[160]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-04T00:00:00"}
