{"id":"https://openalex.org/W7222996590","doi":"https://doi.org/10.48550/arxiv.2610.25863","title":"On Multi-label radio Labelings of Graphs","display_name":"On Multi-label radio Labelings of Graphs","publication_year":2026,"publication_date":"2026-10-19","ids":{"openalex":"https://openalex.org/W7222996590","doi":"https://doi.org/10.48550/arxiv.2610.25863"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.25863","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.25863","pdf_url":"https://arxiv.org/pdf/2610.25863","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":null,"license_id":null,"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/2610.25863","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045655458","display_name":"Olivier Togni","orcid":"https://orcid.org/0000-0001-9510-3595","observed_orcids":["https://orcid.org/0000-0001-9510-3595"]},"institutions":[{"id":"https://openalex.org/I177064439","display_name":"Universit\u00e9 de Bourgogne","ror":"https://ror.org/03k1bsr36","country_code":"FR","type":"education","lineage":["https://openalex.org/I177064439","https://openalex.org/I4405253280"]},{"id":"https://openalex.org/I4405253280","display_name":"Universit\u00e9 Bourgogne Europe","ror":"https://ror.org/00g700j37","country_code":"FR","type":"education","lineage":["https://openalex.org/I4405253280"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Togni, Olivier","raw_affiliation_strings":["LIB UR 7534 , Universit\u00e9 Bourgogne Europe , Dijon , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIB UR 7534 , Universit\u00e9 Bourgogne Europe , Dijon , France","institution_ids":["https://openalex.org/I177064439","https://openalex.org/I4405253280"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5045655458"],"corresponding_institution_ids":["https://openalex.org/I177064439","https://openalex.org/I4405253280"],"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":1.0,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":1.0,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.0,"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":0.0,"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-labeling","display_name":"graph labeling","score":0.824999988079071},{"id":"https://openalex.org/keywords/distance-constraints","display_name":"distance constraints","score":0.3840000033378601},{"id":"https://openalex.org/keywords/paths","display_name":"paths","score":0.8360000252723694},{"id":"https://openalex.org/keywords/cycles","display_name":"cycles","score":0.9869999885559082}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8465999960899353},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.753600001335144},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6359000205993652},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6288999915122986},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.6173999905586243},{"id":"https://openalex.org/C150433608","wikidata":"https://www.wikidata.org/wiki/Q5337633","display_name":"Edge-graceful labeling","level":5,"score":0.5529000163078308},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5116000175476074},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5081999897956848},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47269999980926514},{"id":"https://openalex.org/C2778753569","wikidata":"https://www.wikidata.org/wiki/Q1960395","display_name":"Span (engineering)","level":2,"score":0.4546000063419342},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.44620001316070557},{"id":"https://openalex.org/C166513658","wikidata":"https://www.wikidata.org/wiki/Q5597093","display_name":"Graph labeling","level":5,"score":0.4352000057697296},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.43309998512268066},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.4212999939918518},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.37869998812675476},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.34869998693466187},{"id":"https://openalex.org/C128067373","wikidata":"https://www.wikidata.org/wiki/Q1415372","display_name":"Path graph","level":5,"score":0.3474999964237213},{"id":"https://openalex.org/C161677786","wikidata":"https://www.wikidata.org/wiki/Q2478475","display_name":"Neighbourhood (mathematics)","level":2,"score":0.3285999894142151},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3012999892234802},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C54385418","wikidata":"https://www.wikidata.org/wiki/Q2742711","display_name":"Distance","level":4,"score":0.2766999900341034},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.2766000032424927},{"id":"https://openalex.org/C23230895","wikidata":"https://www.wikidata.org/wiki/Q104752","display_name":"Coprime integers","level":2,"score":0.25929999351501465}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.25863","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.25863","pdf_url":"https://arxiv.org/pdf/2610.25863","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.25863","doi":"https://doi.org/10.48550/arxiv.2610.25863","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.25863","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:2610.25863","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.25863","pdf_url":"https://arxiv.org/pdf/2610.25863","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":null,"license_id":null,"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/W7222996590.pdf","grobid_xml":"https://content.openalex.org/works/W7222996590.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7125126689"],"related_works":["https://openalex.org/W2056891496","https://openalex.org/W2317341999","https://openalex.org/W4287112002","https://openalex.org/W7033226967","https://openalex.org/W3202122903","https://openalex.org/W7211894303","https://openalex.org/W4324058340","https://openalex.org/W7223144710","https://openalex.org/W2081868613","https://openalex.org/W2121862002"],"abstract_inverted_index":{"We":[0,75,111],"propose":[1,113],"and":[2,18,21,48,57,73,87,97,123],"study":[3],"a":[4,15,29,41,85,114],"multi-labeling":[5],"generalization":[6],"of":[7,12,27,31,51,83],"the":[8,49,68,80,92,104,117,121,129],"$k$-radio":[9],"labeling":[10,86],"problem":[11],"graphs:":[13],"given":[14],"graph":[16],"$G$":[17,28],"integers":[19],"$k$":[20,108],"$m$,":[22],"assign":[23],"to":[24,40],"each":[25],"vertex":[26,42],"set":[30],"$m$":[32],"integer":[33],"labels":[34,38,50],"such":[35,84],"that":[36],"distinct":[37,54],"assigned":[39],"differ":[43,60],"by":[44,61],"at":[45,62],"least":[46,63],"$k+1$,":[47],"any":[52],"two":[53],"vertices":[55,71],"$x$":[56,72],"$y$":[58],"pairwise":[59],"$k+1-d(x,y)$,":[64],"with":[65],"$d(x,y)$":[66],"being":[67],"distance":[69],"between":[70],"$y$.":[74],"prove":[76],"general":[77],"bounds":[78,102],"on":[79,103,120,128],"minimum":[81,105,118],"span":[82,106,119],"more":[88],"refined":[89],"results":[90],"for":[91,116,124],"case":[93],"$k=1$.":[94],"For":[95],"paths":[96],"cycles,":[98],"we":[99],"derive":[100],"sharp":[101],"when":[107],"is":[109],"small.":[110],"finally":[112],"conjecture":[115],"path":[122],"an":[125],"almost-tight":[126],"bound":[127],"cycle.":[130]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-21T00:00:00"}