{"id":"https://openalex.org/W7131875198","doi":"https://doi.org/10.48550/arxiv.2602.23096","title":"Simultaneous separation in bounded degree trees","display_name":"Simultaneous separation in bounded degree trees","publication_year":2026,"publication_date":"2026-02-26","ids":{"openalex":"https://openalex.org/W7131875198","doi":"https://doi.org/10.48550/arxiv.2602.23096"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.23096","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063493591","display_name":"Sagi Snir","orcid":"https://orcid.org/0000-0001-5833-7659"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Snir, Sagi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5026016357","display_name":"Raphael Yuster","orcid":"https://orcid.org/0000-0001-7550-6506"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yuster, Raphael","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5063493591"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T13664","display_name":"Genome Rearrangement Algorithms","score":0.6875,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T13664","display_name":"Genome Rearrangement Algorithms","score":0.6875,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10015","display_name":"Genomics and Phylogenetic Studies","score":0.2506999969482422,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.007400000002235174,"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/bounded-function","display_name":"Bounded function","score":0.6794000267982483},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6506999731063843},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5516999959945679},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5238999724388123},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.4921000003814697},{"id":"https://openalex.org/keywords/phylogenetic-tree","display_name":"Phylogenetic tree","score":0.4593999981880188},{"id":"https://openalex.org/keywords/tree-rearrangement","display_name":"Tree rearrangement","score":0.38019999861717224}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8507999777793884},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7840999960899353},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6794000267982483},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6506999731063843},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5516999959945679},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5238999724388123},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.4921000003814697},{"id":"https://openalex.org/C193252679","wikidata":"https://www.wikidata.org/wiki/Q242125","display_name":"Phylogenetic tree","level":3,"score":0.4593999981880188},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41920000314712524},{"id":"https://openalex.org/C53208351","wikidata":"https://www.wikidata.org/wiki/Q7837630","display_name":"Tree rearrangement","level":4,"score":0.38019999861717224},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.37880000472068787},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3391999900341034},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.32919999957084656},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.31209999322891235},{"id":"https://openalex.org/C100560664","wikidata":"https://www.wikidata.org/wiki/Q3608019","display_name":"K-ary tree","level":4,"score":0.3050000071525574},{"id":"https://openalex.org/C41168302","wikidata":"https://www.wikidata.org/wiki/Q3772859","display_name":"Computational phylogenetics","level":5,"score":0.28360000252723694},{"id":"https://openalex.org/C84927040","wikidata":"https://www.wikidata.org/wiki/Q6057306","display_name":"Interval tree","level":4,"score":0.27239999175071716},{"id":"https://openalex.org/C11829167","wikidata":"https://www.wikidata.org/wiki/Q751292","display_name":"Random binary tree","level":3,"score":0.2529999911785126}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.23096","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.23096","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.23096","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":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.23096","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"It":[0],"follows":[1],"from":[2],"a":[3,18,25,70,80,159],"classical":[4],"result":[5,146],"of":[6,52,56,169],"Jordan":[7],"that":[8,125,129,148],"every":[9],"tree":[10,43,85,163],"with":[11,63],"maximum":[12,64,104],"degree":[13,65],"at":[14,66,99,161,171],"most":[15,67],"$r$":[16],"containing":[17,69],"vertex":[19,54,72],"set":[20,73],"labeled":[21,74],"by":[22,41,75,95,105],"$[n]$,":[23,76],"has":[24],"single-edge":[26,81],"cut":[27,82,98],"which":[28,36,86,131,164],"separates":[29,165],"two":[30,150,166],"subsets":[31],"$A,B":[32,90],"\\subset":[33,91],"[n]$":[34,92],"for":[35,79],"$\\min\\{|A|,|B|\\}":[37],"\\ge":[38],"(n-1)/r$.":[39],"Motivated":[40],"the":[42,50,96,109],"dissimilarity":[44],"problem":[45],"in":[46,83,142],"phylogenetics,":[47],"we":[48,77,123],"consider":[49],"case":[51,137],"separating":[53],"sets":[55,168],"{\\em":[57],"several}":[58],"trees:":[59],"Given":[60],"$k$":[61],"trees":[62,154],"$r$,":[68],"common":[71],"ask":[78],"each":[84,100,162],"maximizes":[87],"$min\\{|A|,|B|\\}$":[88],"where":[89],"are":[93,179],"separated":[94],"corresponding":[97],"tree.":[101],"Denoting":[102],"this":[103],"$f(r,k,n)$":[106],"and":[107,127,144,176],"considering":[108],"limit":[110],"$f(r,k)":[111],"=":[112],"\\lim_{n":[113],"\\rightarrow":[114],"\\infty}":[115],"f(r,k,n)/n$":[116],"(which":[117],"is":[118,132,139],"shown":[119],"to":[120],"always":[121],"exist)":[122],"determine":[124,128],"$f(r,2)=\\frac{1}{2r}$":[126],"$f(3,3)=\\frac{2}{27}$,":[130],"already":[133],"quite":[134],"intricate.":[135],"The":[136],"$r=3$":[138],"especially":[140],"interesting":[141],"phylogenetics":[143],"our":[145],"implies":[147],"any":[149],"(three)":[151],"binary":[152],"phylogenetic":[153],"over":[155],"$n$":[156],"taxa":[157,167],"have":[158],"split":[160],"order":[170],"least":[172],"$n/6$":[173],"(resp.":[174],"$2n/27$),":[175],"these":[177],"bounds":[178],"asymptotically":[180],"tight.":[181]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2026-02-28T00:00:00"}
