{"id":"https://openalex.org/W4416596161","doi":"https://doi.org/10.4230/lipics.itcs.2026.1","title":"Triangle Detection in H-Free Graphs","display_name":"Triangle Detection in H-Free Graphs","publication_year":2025,"publication_date":"2025-11-21","ids":{"openalex":"https://openalex.org/W4416596161","doi":"https://doi.org/10.4230/lipics.itcs.2026.1"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2511.17224","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2511.17224","pdf_url":"https://arxiv.org/pdf/2511.17224","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":"text"},"type":"article","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2511.17224","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051832024","display_name":"Amir Abboud","orcid":"https://orcid.org/0000-0002-0502-4517"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Abboud, Amir","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091434760","display_name":"Ron Safier","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Safier, Ron","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5060641522","display_name":"Nathan Wallheimer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wallheimer, Nathan","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5051832024"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.36919246,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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":0.3716999888420105,"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":0.3716999888420105,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.1728000044822693,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.10300000011920929,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/generalization","display_name":"Generalization","score":0.48899999260902405},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4632999897003174},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.4325999915599823},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4235999882221222},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.3718000054359436},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.3601999878883362},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.3562000095844269}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.718500018119812},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6922000050544739},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.48899999260902405},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4632999897003174},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.4325999915599823},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4262999892234802},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4235999882221222},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.3718000054359436},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36880001425743103},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3601999878883362},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3562000095844269},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.34630000591278076},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3183000087738037},{"id":"https://openalex.org/C2988809283","wikidata":"https://www.wikidata.org/wiki/Q1514868","display_name":"Combinatorial algorithms","level":2,"score":0.3131999969482422},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.3077000081539154},{"id":"https://openalex.org/C2983226441","wikidata":"https://www.wikidata.org/wiki/Q3115621","display_name":"Vertex connectivity","level":4,"score":0.30239999294281006},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25540000200271606},{"id":"https://openalex.org/C3017489831","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Running time","level":2,"score":0.25440001487731934}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:arXiv.org:2511.17224","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2511.17224","pdf_url":"https://arxiv.org/pdf/2511.17224","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":"text"},{"id":"pmh:oai:drops-oai.dagstuhl.de:25288","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.1","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol362-itcs2026/LIPIcs.ITCS.2026.1/LIPIcs.ITCS.2026.1.pdf","source":{"id":"https://openalex.org/S4306402524","display_name":"Leibniz-Zentrum f\u00fcr Informatik (Schloss Dagstuhl)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"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":"doi:10.48550/arxiv.2511.17224","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2511.17224","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"doi:10.4230/lipics.itcs.2026.1","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.itcs.2026.1","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2511.17224","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2511.17224","pdf_url":"https://arxiv.org/pdf/2511.17224","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,150,233],"initiate":[1],"the":[2,60,78,81,93,143,146,177,209,219,227,263,268,286,291],"study":[3],"of":[4,80,114,122,193,211,213,230,265,288],"combinatorial":[5,87,108,245,272],"algorithms":[6,238],"for":[7,110,118,183,190,202,247,255],"Triangle":[8,236],"Detection":[9,237],"in":[10,104,128,176,252,267,277,290],"H-free":[11],"graphs.":[12],"The":[13],"goal":[14],"is":[15,69,89,215,262,285],"to":[16,46,140,161,167,196],"decide":[17],"if":[18,67],"a":[19,23,28,31,51,56,105,111,168,174,187],"graph":[20],"that":[21,37,66,102,163,171,239,250,275],"forbids":[22],"fixed":[24],"pattern":[25,121],"H":[26,68,214],"as":[27],"subgraph":[29],"contains":[30,73],"triangle,":[32,77],"using":[33],"only":[34],"\"combinatorial\"":[35],"methods":[36],"notably":[38],"exclude":[39],"fast":[40],"matrix":[41],"multiplication.":[42],"Our":[43],"work":[44],"aims":[45],"classify":[47],"which":[48,205],"patterns":[49,162,192],"admit":[50],"subcubic":[52],"speedup,":[53],"working":[54],"towards":[55],"dichotomy":[57,188],"theorem.":[58],"On":[59,92],"lower":[61],"bound":[62,95],"side,":[63,96],"we":[64,97,224],"show":[65],"not":[70],"3-colorable":[71],"or":[72],"more":[74],"than":[75,218],"one":[76],"complexity":[79],"problem":[82],"remains":[83],"unchanged,":[84],"and":[85],"no":[86],"speedup":[88],"likely":[90],"possible.":[91],"upper":[94],"develop":[98],"an":[99,119],"embedding":[100],"approach":[101],"results":[103],"strongly":[106],"subcubic,":[107],"algorithm":[109,126,137,201,246,274],"rich":[112],"class":[113],"\"embeddable\"":[115],"patterns.":[116],"Specifically,":[117],"embeddable":[120,165,203],"size":[123,194],"k,":[124],"our":[125,181],"runs":[127,206,251,276],"\u00d5(n^{3-1/(2^{k-3)}})":[129],"time,":[130,282],"where":[131,260,283],"\u00d5(\u22c5)":[132],"hides":[133],"poly-logarithmic":[134],"factors.":[135],"This":[136,179],"also":[138],"extends":[139],"listing":[141],"all":[142,191],"triangles":[144],"within":[145],"same":[147],"time":[148,254],"bound.":[149],"supplement":[151],"this":[152],"main":[153],"result":[154],"with":[155],"two":[156],"generalizations:":[157],"-":[158,198,243,270],"A":[159,244,271],"generalization":[160],"are":[164,240],"up":[166,195],"single":[169],"obstacle":[170],"arises":[172],"from":[173],"triangle":[175],"pattern.":[178],"completes":[180],"classification":[182],"small":[184],"patterns,":[185,204],"yielding":[186],"theorem":[189],"eight.":[197],"An":[199],"H-sensitive":[200],"faster":[207],"when":[208],"number":[210,264,287],"copies":[212],"significantly":[216],"smaller":[217],"maximum":[220],"possible":[221],"\u03a9(n^{k}).":[222],"Finally,":[223],"focus":[225],"on":[226],"special":[228],"case":[229],"odd":[231],"cycles.":[232],"present":[234],"specialized":[235],"very":[241],"efficient:":[242],"C_{2k+1}-free":[248],"graphs":[249],"\u00d5(m+n^{1+2/k})":[253],"every":[256],"k":[257],"\u2265":[258],"2,":[259],"m":[261],"edges":[266],"graph.":[269,292],"C\u2085-sensitive":[273],"\u00d5(n\u00b2":[278],"+":[279],"n^{4/3}":[280],"t^{1/3})":[281],"t":[284],"5-cycles":[289]},"counts_by_year":[],"updated_date":"2026-03-23T07:41:27.035349","created_date":"2025-11-25T00:00:00"}