{"id":"https://openalex.org/W7212018669","doi":"https://doi.org/10.48550/arxiv.2609.06860","title":"Bridge numbers of virtual graphs and handlebody-links","display_name":"Bridge numbers of virtual graphs and handlebody-links","publication_year":2026,"publication_date":"2026-09-06","ids":{"openalex":"https://openalex.org/W7212018669","doi":"https://doi.org/10.48550/arxiv.2609.06860"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.06860","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.06860","pdf_url":"https://arxiv.org/pdf/2609.06860","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/2609.06860","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151059840","display_name":"Nikolaos Chantis","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chantis, Nikolaos","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5065191712","display_name":"Puttipong Pongtanapaisan","orcid":"https://orcid.org/0000-0003-2700-9606","observed_orcids":["https://orcid.org/0000-0003-2700-9606"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pongtanapaisan, Puttipong","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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.00039999998989515007,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/biquandles","display_name":"biquandles","score":0.9850000143051147},{"id":"https://openalex.org/keywords/cubic-graphs","display_name":"cubic graphs","score":0.8320000171661377},{"id":"https://openalex.org/keywords/regular-neighborhoods","display_name":"regular neighborhoods","score":0.5630000233650208},{"id":"https://openalex.org/keywords/spatial-graphs","display_name":"spatial graphs","score":0.7549999952316284},{"id":"https://openalex.org/keywords/euler-characteristic","display_name":"Euler characteristic","score":0.4729999899864197}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7599999904632568},{"id":"https://openalex.org/C100776233","wikidata":"https://www.wikidata.org/wiki/Q2532492","display_name":"Bridge (graph theory)","level":2,"score":0.6912999749183655},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.48339998722076416},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46709999442100525},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.4625999927520752},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.44929999113082886},{"id":"https://openalex.org/C196433757","wikidata":"https://www.wikidata.org/wiki/Q852973","display_name":"Euler characteristic","level":2,"score":0.43950000405311584},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.41280001401901245},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.36550000309944153},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.3635999858379364},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3481000065803528},{"id":"https://openalex.org/C2778753846","wikidata":"https://www.wikidata.org/wiki/Q6554239","display_name":"Link (geometry)","level":2,"score":0.3285999894142151},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.32100000977516174},{"id":"https://openalex.org/C159867001","wikidata":"https://www.wikidata.org/wiki/Q904942","display_name":"Topological index","level":2,"score":0.28049999475479126},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.27000001072883606},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.25540000200271606}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.06860","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.06860","pdf_url":"https://arxiv.org/pdf/2609.06860","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.2609.06860","doi":"https://doi.org/10.48550/arxiv.2609.06860","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.06860","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:2609.06860","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.06860","pdf_url":"https://arxiv.org/pdf/2609.06860","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/W7212018669.pdf","grobid_xml":"https://content.openalex.org/works/W7212018669.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W3038099888","https://openalex.org/W4413217240","https://openalex.org/W7124739154"],"related_works":["https://openalex.org/W4414495843","https://openalex.org/W4414830496","https://openalex.org/W7216244648","https://openalex.org/W615602220","https://openalex.org/W2950967079","https://openalex.org/W7096582124","https://openalex.org/W84818571","https://openalex.org/W4405713959","https://openalex.org/W2060813514","https://openalex.org/W2057923619"],"abstract_inverted_index":{"We":[0,12,67],"study":[1],"bridge":[2,21,26,65,72,93,97,115],"indices":[3,73,116],"of":[4,44,57,76,99,107],"graphs,":[5,7],"virtual":[6,14],"and":[8,23,95,113],"their":[9],"handlebody":[10],"classes.":[11],"construct":[13,52],"ravels":[15,75],"for":[16,37,74],"which":[17],"the":[18,96],"difference":[19,89,118],"between":[20,90],"index":[22,27,94,98],"weighted":[24],"overpass":[25],"is":[28,119],"unbounded.":[29,120],"The":[30],"lower":[31],"bound":[32],"uses":[33],"exponentially":[34],"many":[35],"colorings":[36],"one":[38,58],"fixed":[39,59,78],"flow":[40],"in":[41],"a":[42],"$\\Z_2$-family":[43],"biquandles.":[45],"For":[46],"each":[47,77],"negative":[48],"Euler":[49],"characteristic":[50],"we":[51],"classical":[53],"almost":[54,83],"unknotted":[55,84],"graphs":[56],"trivalent":[60],"graph":[61],"with":[62],"arbitrarily":[63],"large":[64],"index.":[66],"also":[68],"obtain":[69],"unbounded":[70,88],"even":[71],"bouquet":[79],"rank.":[80],"A":[81],"separate":[82],"family":[85],"has":[86],"an":[87],"its":[91,100],"spatial-graph":[92],"regular":[101],"neighborhood.":[102],"Finally,":[103],"edge":[104],"connected":[105],"sums":[106],"Suzuki":[108],"curves":[109],"give":[110],"exact":[111],"constrained":[112],"unconstrained":[114],"whose":[117]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-10T00:00:00"}
