{"id":"https://openalex.org/W7223389149","doi":"https://doi.org/10.48550/arxiv.2610.30165","title":"Connected graphs with equal independence number and radius","display_name":"Connected graphs with equal independence number and radius","publication_year":2026,"publication_date":"2026-10-14","ids":{"openalex":"https://openalex.org/W7223389149","doi":"https://doi.org/10.48550/arxiv.2610.30165"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.30165","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.30165","pdf_url":"https://arxiv.org/pdf/2610.30165","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/2610.30165","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101769903","display_name":"Xingzhi Zhan","orcid":"https://orcid.org/0000-0001-7694-1286","observed_orcids":["https://orcid.org/0000-0001-7694-1286"]},"institutions":[{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhan, Xingzhi","raw_affiliation_strings":["Department of Mathematics , Key Laboratory of MEA (Ministry of Education) and Shanghai Key Laboratory of PMMP , East China Normal University , Shanghai 200241 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Key Laboratory of MEA (Ministry of Education) and Shanghai Key Laboratory of PMMP , East China Normal University , Shanghai 200241 , China","institution_ids":["https://openalex.org/I66867065"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101769903"],"corresponding_institution_ids":["https://openalex.org/I66867065"],"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":0.9678000211715698,"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":0.9678000211715698,"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/T11476","display_name":"Graph theory and applications","score":0.021299999207258224,"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"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.0044999998062849045,"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/independence-number","display_name":"independence number","score":0.9010000228881836},{"id":"https://openalex.org/keywords/graph-radius","display_name":"graph radius","score":0.9599999785423279},{"id":"https://openalex.org/keywords/traceable-graphs","display_name":"traceable graphs","score":0.9290000200271606},{"id":"https://openalex.org/keywords/hamiltonian-graphs","display_name":"Hamiltonian graphs","score":0.9449999928474426},{"id":"https://openalex.org/keywords/hamiltonian-connected-graphs","display_name":"Hamiltonian-connected graphs","score":0.9020000100135803},{"id":"https://openalex.org/keywords/pancyclic-graphs","display_name":"pancyclic graphs","score":0.9739999771118164},{"id":"https://openalex.org/keywords/biconnected-graphs","display_name":"2-connected graphs","score":0.9539999961853027},{"id":"https://openalex.org/keywords/3-connected-graphs","display_name":"3-connected graphs","score":0.9940000176429749},{"id":"https://openalex.org/keywords/graph-connectivity","display_name":"graph connectivity","score":0.5550000071525574},{"id":"https://openalex.org/keywords/graph-invariants","display_name":"graph invariants","score":0.37599998712539673}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8016999959945679},{"id":"https://openalex.org/C2984853995","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independence number","level":3,"score":0.76910001039505},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6794999837875366},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.6266000270843506},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5468000173568726},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4934999942779541},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.46070000529289246},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.4424999952316284},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.36340001225471497},{"id":"https://openalex.org/C100500283","wikidata":"https://www.wikidata.org/wiki/Q1374495","display_name":"Cubic graph","level":5,"score":0.3138999938964844},{"id":"https://openalex.org/C2777724877","wikidata":"https://www.wikidata.org/wiki/Q2548661","display_name":"Crossing number (knot theory)","level":3,"score":0.2962000072002411},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.29490000009536743},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.2858000099658966},{"id":"https://openalex.org/C137618395","wikidata":"https://www.wikidata.org/wiki/Q576728","display_name":"Winding number","level":2,"score":0.274399995803833},{"id":"https://openalex.org/C140752511","wikidata":"https://www.wikidata.org/wiki/Q905837","display_name":"Graph minor","level":5,"score":0.27390000224113464},{"id":"https://openalex.org/C18359143","wikidata":"https://www.wikidata.org/wiki/Q7888149","display_name":"Maximal independent set","level":5,"score":0.2603999972343445},{"id":"https://openalex.org/C168291704","wikidata":"https://www.wikidata.org/wiki/Q902252","display_name":"Complement graph","level":5,"score":0.25209999084472656},{"id":"https://openalex.org/C32972407","wikidata":"https://www.wikidata.org/wiki/Q1187620","display_name":"Perfect graph","level":5,"score":0.25049999356269836}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.30165","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.30165","pdf_url":"https://arxiv.org/pdf/2610.30165","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.2610.30165","doi":"https://doi.org/10.48550/arxiv.2610.30165","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.30165","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.30165","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.30165","pdf_url":"https://arxiv.org/pdf/2610.30165","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":[{"id":"https://openalex.org/G1609915050","display_name":null,"funder_award_id":"22DZ2229014","funder_id":"https://openalex.org/F4320321885","funder_display_name":"Science and Technology Commission of Shanghai Municipality"},{"id":"https://openalex.org/G486494320","display_name":null,"funder_award_id":"12271170","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7270659173","display_name":null,"funder_award_id":"22DZ2229014","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321885","display_name":"Science and Technology Commission of Shanghai Municipality","ror":"https://ror.org/03kt66j61"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223389149.pdf","grobid_xml":"https://content.openalex.org/works/W7223389149.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2072220480","https://openalex.org/W2805593026","https://openalex.org/W4299568263","https://openalex.org/W3036047107","https://openalex.org/W2962745304","https://openalex.org/W2169146866","https://openalex.org/W2891688742","https://openalex.org/W1997604000","https://openalex.org/W28227665","https://openalex.org/W7136708074"],"abstract_inverted_index":{"A":[0],"classical":[1],"theorem":[2,45],"states":[3],"that":[4,24],"the":[5,86],"independence":[6,30,62,74],"number":[7,31,63,75],"of":[8,43,53,89],"any":[9],"connected":[10,26],"graph":[11,27,59,71],"is":[12,34,66,78],"at":[13],"least":[14],"its":[15],"radius.":[16],"In":[17],"2007,":[18],"DeLaVi\u00f1a,":[19],"Pepper,":[20],"and":[21,32,46,64,76,80],"Waller":[22],"proved":[23],"every":[25],"with":[28,60,72],"equal":[29,61,73],"radius":[33,65,77],"traceable.":[35],"We":[36],"first":[37],"give":[38],"a":[39],"new":[40],"short":[41],"proof":[42],"this":[44],"then":[47],"prove":[48],"two":[49],"results":[50],"for":[51],"graphs":[52],"higher":[54],"connectivity.":[55],"(1)":[56],"Every":[57,69],"2-connected":[58],"Hamiltonian.":[67],"(2)":[68],"3-connected":[70],"Hamiltonian-connected":[79],"pancyclic.":[81],"Several":[82],"lemmas":[83],"used":[84],"in":[85],"proofs":[87],"are":[88],"independent":[90],"interest.":[91]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-24T00:00:00"}