{"id":"https://openalex.org/W2133862292","doi":"https://doi.org/10.37236/1109","title":"Identifying $X$-Trees with Few Characters","display_name":"Identifying $X$-Trees with Few Characters","publication_year":2006,"publication_date":"2006-09-28","ids":{"openalex":"https://openalex.org/W2133862292","doi":"https://doi.org/10.37236/1109","mag":"2133862292"},"language":"en","primary_location":{"id":"doi:10.37236/1109","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1109","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r83/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r83/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016565949","display_name":"Magnus Bordewich","orcid":"https://orcid.org/0000-0003-1475-8923"},"institutions":[{"id":"https://openalex.org/I190082696","display_name":"Durham University","ror":"https://ror.org/01v29qb04","country_code":"GB","type":"education","lineage":["https://openalex.org/I190082696"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Magnus Bordewich","raw_affiliation_strings":["Department of Computer Science Durham University, Durham DH1 3LE, United Kingdom","Durham University"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science Durham University, Durham DH1 3LE, United Kingdom","institution_ids":["https://openalex.org/I190082696"]},{"raw_affiliation_string":"Durham University","institution_ids":["https://openalex.org/I190082696"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049682492","display_name":"Charles Semple","orcid":"https://orcid.org/0000-0002-4315-4195"},"institutions":[{"id":"https://openalex.org/I185492890","display_name":"University of Canterbury","ror":"https://ror.org/03y7q9t39","country_code":"NZ","type":"education","lineage":["https://openalex.org/I185492890"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Charles Semple","raw_affiliation_strings":["Department of Mathematics and Statistics","University of Canterbury Christchurch, New Zealand","University of Canterbury,"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics","institution_ids":[]},{"raw_affiliation_string":"University of Canterbury Christchurch, New Zealand","institution_ids":["https://openalex.org/I185492890"]},{"raw_affiliation_string":"University of Canterbury,","institution_ids":["https://openalex.org/I185492890"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035720494","display_name":"Mike Steel","orcid":"https://orcid.org/0000-0001-7015-4644"},"institutions":[{"id":"https://openalex.org/I185492890","display_name":"University of Canterbury","ror":"https://ror.org/03y7q9t39","country_code":"NZ","type":"education","lineage":["https://openalex.org/I185492890"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Mike Steel","raw_affiliation_strings":["Department of Mathematics and Statistics","University of Canterbury Christchurch, New Zealand","University of Canterbury,"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics","institution_ids":[]},{"raw_affiliation_string":"University of Canterbury Christchurch, New Zealand","institution_ids":["https://openalex.org/I185492890"]},{"raw_affiliation_string":"University of Canterbury,","institution_ids":["https://openalex.org/I185492890"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5016565949"],"corresponding_institution_ids":["https://openalex.org/I190082696"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.13190463,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"13","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10015","display_name":"Genomics and Phylogenetic Studies","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T10015","display_name":"Genomics and Phylogenetic Studies","score":0.9990000128746033,"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/T10012","display_name":"Genetic diversity and population structure","score":0.9702000021934509,"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/T11354","display_name":"Evolution and Paleontology Studies","score":0.949999988079071,"subfield":{"id":"https://openalex.org/subfields/1911","display_name":"Paleontology"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8489948511123657},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8300979137420654},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.7470278143882751},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5879218578338623},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5456557273864746},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.49533024430274963},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4696086347103119},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.12128010392189026},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05393907427787781},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.04382479190826416}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8489948511123657},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8300979137420654},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.7470278143882751},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5879218578338623},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5456557273864746},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.49533024430274963},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4696086347103119},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.12128010392189026},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05393907427787781},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.04382479190826416},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":9,"locations":[{"id":"doi:10.37236/1109","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1109","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r83/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:dro.dur.ac.uk.OAI2:6314","is_oa":false,"landing_page_url":"http://dro.dur.ac.uk/6314/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196258","display_name":"Durham Research Online (Durham University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I190082696","host_organization_name":"Durham University","host_organization_lineage":["https://openalex.org/I190082696"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"The electronic journal of combinatorics, 2006, Vol.13(1), pp.R83 [Peer Reviewed Journal]","raw_type":"Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.387.7359","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.387.7359","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.canterbury.ac.nz/~c.semple/papers/BorSS06.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.605.5068","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.605.5068","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://dro.dur.ac.uk/6314/1/6314.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.67.2446","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.67.2446","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.dur.ac.uk/m.j.r.bordewich/Bordewich2006-e.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.94.1906","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.94.1906","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_13/PDF/v13i1r83.pdf","raw_type":"text"},{"id":"pmh:oai:durham-repository.worktribe.com:1522690","is_oa":true,"landing_page_url":"https://durham-repository.worktribe.com/output/1522690","pdf_url":null,"source":{"id":"https://openalex.org/S4306400188","display_name":"Durham Research Online (Durham University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I190082696","host_organization_name":"Durham University","host_organization_lineage":["https://openalex.org/I190082696"],"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":"publishedVersion"},{"id":"pmh:oai:ir.canterbury.ac.nz:10092/12223","is_oa":false,"landing_page_url":"http://hdl.handle.net/10092/12223","pdf_url":null,"source":{"id":"https://openalex.org/S4306401103","display_name":"University of Canterbury Research Repository (University of Canterbury)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I185492890","host_organization_name":"University of Canterbury","host_organization_lineage":["https://openalex.org/I185492890"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Discussion / Working Papers"},{"id":"pmh:oai:ir.canterbury.ac.nz:10092/52","is_oa":false,"landing_page_url":"http://hdl.handle.net/10092/52","pdf_url":null,"source":{"id":"https://openalex.org/S4306401103","display_name":"University of Canterbury Research Repository (University of Canterbury)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I185492890","host_organization_name":"University of Canterbury","host_organization_lineage":["https://openalex.org/I185492890"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.37236/1109","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1109","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r83/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310502","display_name":"University of Canterbury","ror":"https://ror.org/03y7q9t39"},{"id":"https://openalex.org/F4320335369","display_name":"Marsden Fund","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2133862292.pdf","grobid_xml":"https://content.openalex.org/works/W2133862292.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W100917773","https://openalex.org/W123339781","https://openalex.org/W1596422325","https://openalex.org/W1982453483","https://openalex.org/W2019662708","https://openalex.org/W2120707543"],"related_works":["https://openalex.org/W4318195686","https://openalex.org/W2975999359","https://openalex.org/W3161230432","https://openalex.org/W4287173569","https://openalex.org/W2796561647","https://openalex.org/W4313513739","https://openalex.org/W3119693376","https://openalex.org/W3182422617","https://openalex.org/W2244208494","https://openalex.org/W2950159329"],"abstract_inverted_index":{"Previous":[0],"work":[1],"has":[2],"shown":[3],"the":[4,31,47,57],"perhaps":[5],"surprising":[6],"result":[7],"that,":[8],"for":[9],"any":[10,51],"binary":[11],"phylogenetic":[12],"tree":[13],"${\\cal":[14,25,35,54,64],"T}$,":[15,55],"there":[16],"is":[17,37,46,66],"a":[18,71],"set":[19],"of":[20,50,60],"four":[21],"characters":[22,61],"that":[23,43,62],"define":[24],"T}$.":[26],"Here":[27],"we":[28],"deal":[29],"with":[30],"general":[32],"case,":[33],"where":[34],"T}$":[36,65],"an":[38],"arbitrary":[39],"$X$-tree.":[40],"We":[41],"show":[42],"if":[44],"$d$":[45],"maximum":[48],"degree":[49],"vertex":[52],"in":[53],"then":[56],"minimum":[58],"number":[59],"identify":[63],"$\\log_2":[67],"d$":[68],"(up":[69],"to":[70],"small":[72],"multiplicative":[73],"constant).":[74]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}