{"id":"https://openalex.org/W2079730460","doi":"https://doi.org/10.1137/s0895480193250162","title":"The Total Interval Number of a Graph II: Trees and Complexity","display_name":"The Total Interval Number of a Graph II: Trees and Complexity","publication_year":1996,"publication_date":"1996-05-01","ids":{"openalex":"https://openalex.org/W2079730460","doi":"https://doi.org/10.1137/s0895480193250162","mag":"2079730460"},"language":"en","primary_location":{"id":"doi:10.1137/s0895480193250162","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480193250162","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050797036","display_name":"Thomas M. Kratzke","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Thomas M. Kratzke","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5017595199","display_name":"Douglas B. West","orcid":"https://orcid.org/0000-0001-8818-1667"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Douglas B. West","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5050797036"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5153,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.6761425,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"9","issue":"2","first_page":"339","last_page":"348"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9986000061035156,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9957000017166138,"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/combinatorics","display_name":"Combinatorics","score":0.9006441831588745},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8494106531143188},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5523496270179749},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5163944363594055},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.47494959831237793},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.44368046522140503},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4208952486515045},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.41802671551704407}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9006441831588745},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8494106531143188},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5523496270179749},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5163944363594055},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.47494959831237793},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.44368046522140503},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4208952486515045},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.41802671551704407},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0895480193250162","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480193250162","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.137.5982","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.137.5982","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uiuc.edu/~west/pubs/titrees.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W179863491","https://openalex.org/W1983151348","https://openalex.org/W1985260677","https://openalex.org/W2005906639","https://openalex.org/W2066371787","https://openalex.org/W2074710925","https://openalex.org/W2076027639","https://openalex.org/W2078480613","https://openalex.org/W2087818742","https://openalex.org/W2112631288","https://openalex.org/W2141660592"],"related_works":["https://openalex.org/W1971174658","https://openalex.org/W2099195351","https://openalex.org/W4256429076","https://openalex.org/W2012063272","https://openalex.org/W2348092930","https://openalex.org/W2062850566","https://openalex.org/W4308716484","https://openalex.org/W2098284475","https://openalex.org/W2587900963","https://openalex.org/W2132864204"],"abstract_inverted_index":{"A":[0],"multiple-interval":[1],"representation":[2,47],"of":[3,13,37,41,48,64,73,80,121,140,157,162,170],"a":[4,11,46,110,119,158,160,167],"simple":[5],"graph":[6],"G":[7],"assigns":[8],"each":[9,74],"vertex":[10],"union":[12],"disjoint":[14],"real":[15],"intervals":[16,42,130],"so":[17],"that":[18,68,99],"vertices":[19],"are":[20],"adjacent":[21],"if":[22,25],"and":[23,95,118,166],"only":[24],"their":[26],"assigned":[27],"sets":[28],"intersect.":[29],"The":[30],"total":[31,39],"interval":[32],"number$I(G)$":[33],"is":[34,60,102],"the":[35,38,61,78,122,137,163,171],"minimum":[36,62],"number":[40,63],"used":[43],"in":[44],"such":[45],"G.":[49],"For":[50],"triangle-free":[51,91],"graphs,":[52],"$I(G)":[53,82,141],"=":[54,83],"|":[55,84,86,127],"E(G)":[56,85,126],"|+t(G)$,":[57],"where":[58],"$t(G)$":[59],"pairwise":[65],"edge-disjoint":[66],"trails":[67],"together":[69],"contain":[70],"an":[71,96],"endpoint":[72],"edge.":[75],"This":[76],"yields":[77,109],"NP-completeness":[79],"testing":[81],"+":[87,128,176],"1$":[88],"(even":[89],"for":[90,104,116,131,149,180],"3-regular":[92],"planar":[93],"graphs)":[94],"alternative":[97],"proof":[98,169],"HAMILTONIAN":[100],"CYCLE":[101],"NP-complete":[103],"line":[105],"graphs.":[106,182],"It":[107],"also":[108],"linear-time":[111],"algorithm":[112],"to":[113],"compute":[114],"$I(G)$":[115],"trees":[117,123,151],"characterization":[120,161],"requiring":[124],"$|":[125],"t$":[129],"fixed":[132],"t.":[133],"Further":[134],"corollaries":[135],"include":[136],"Aigner-Andreae":[138],"bound":[139,173],"\\leq":[142],"\\lfloor":[143],"{(5n":[144],"-":[145],"3)/4}":[146],"\\rfloor":[147,178],"$":[148,179],"n-vertex":[150],"(achieved":[152],"by":[153],"subdividing":[154],"every":[155],"edge":[156],"star),":[159],"extremal":[164,172],"trees,":[165],"shorter":[168],"$\\lfloor":[174],"{(5m":[175],"2)/4}":[177],"connected":[181]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}