{"id":"https://openalex.org/W7140308067","doi":"https://doi.org/10.48550/arxiv.2603.22993","title":"Backward Arcs in Hamilton Oriented Cycles and Paths in Directed Graphs with Independence Number Two","display_name":"Backward Arcs in Hamilton Oriented Cycles and Paths in Directed Graphs with Independence Number Two","publication_year":2026,"publication_date":"2026-03-24","ids":{"openalex":"https://openalex.org/W7140308067","doi":"https://doi.org/10.48550/arxiv.2603.22993"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.22993","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.22993","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":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.22993","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5130545595","display_name":"S. Gerke","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gerke, S.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130567134","display_name":"Q. Guo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guo, Q.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130542527","display_name":"G. Gutin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gutin, G.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130547126","display_name":"Y. Hao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hao, Y.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130546884","display_name":"W. Veeranonchai","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Veeranonchai, W.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5130609205","display_name":"A. Yeo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yeo, A.","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5130545595"],"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/T10374","display_name":"Advanced Graph Theory Research","score":0.7825000286102295,"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":0.7825000286102295,"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":0.12449999898672104,"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":0.021400000900030136,"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/digraph","display_name":"Digraph","score":0.9204000234603882},{"id":"https://openalex.org/keywords/hamiltonian-path","display_name":"Hamiltonian path","score":0.7293000221252441},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.629800021648407},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5400000214576721},{"id":"https://openalex.org/keywords/undirected-graph","display_name":"Undirected graph","score":0.460999995470047},{"id":"https://openalex.org/keywords/feedback-arc-set","display_name":"Feedback arc set","score":0.45570001006126404},{"id":"https://openalex.org/keywords/independence-number","display_name":"Independence number","score":0.44369998574256897},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.41819998621940613},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4180000126361847}],"concepts":[{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.9204000234603882},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8382999897003174},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7906000018119812},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.7293000221252441},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.629800021648407},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5400000214576721},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5178999900817871},{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.460999995470047},{"id":"https://openalex.org/C157951044","wikidata":"https://www.wikidata.org/wiki/Q1400910","display_name":"Feedback arc set","level":5,"score":0.45570001006126404},{"id":"https://openalex.org/C2984853995","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independence number","level":3,"score":0.44369998574256897},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.41819998621940613},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4180000126361847},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.4146000146865845},{"id":"https://openalex.org/C83415579","wikidata":"https://www.wikidata.org/wiki/Q161973","display_name":"Arc (geometry)","level":2,"score":0.41449999809265137},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.37720000743865967},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.35420000553131104},{"id":"https://openalex.org/C38754835","wikidata":"https://www.wikidata.org/wiki/Q2003238","display_name":"Strongly connected component","level":2,"score":0.34549999237060547},{"id":"https://openalex.org/C58228413","wikidata":"https://www.wikidata.org/wiki/Q15704639","display_name":"Induced path","level":5,"score":0.3379000127315521},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.3174999952316284},{"id":"https://openalex.org/C128067373","wikidata":"https://www.wikidata.org/wiki/Q1415372","display_name":"Path graph","level":5,"score":0.30550000071525574},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2948000133037567},{"id":"https://openalex.org/C53052385","wikidata":"https://www.wikidata.org/wiki/Q17104046","display_name":"Mixed graph","level":5,"score":0.2847999930381775},{"id":"https://openalex.org/C125080357","wikidata":"https://www.wikidata.org/wiki/Q45715","display_name":"Complete graph","level":3,"score":0.2799000144004822},{"id":"https://openalex.org/C74197172","wikidata":"https://www.wikidata.org/wiki/Q1195339","display_name":"Directed acyclic graph","level":2,"score":0.27300000190734863},{"id":"https://openalex.org/C22251595","wikidata":"https://www.wikidata.org/wiki/Q670036","display_name":"Arc length","level":3,"score":0.2694000005722046},{"id":"https://openalex.org/C148364342","wikidata":"https://www.wikidata.org/wiki/Q948887","display_name":"Wheel graph","level":5,"score":0.2612999975681305},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.25619998574256897},{"id":"https://openalex.org/C1465435","wikidata":"https://www.wikidata.org/wiki/Q2916352","display_name":"Longest path problem","level":4,"score":0.25099998712539673}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.22993","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.22993","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"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.22993","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.22993","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":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":{"In":[0],"a":[1,8,37,45,61,104,125,144],"digraph":[2,77,119,138],"$D=(V,A)$,":[3],"an":[4],"oriented":[5,96,106,127,146],"path":[6,147],"is":[7,36,44,52,68,78,85],"sequence":[9],"$P=x_1x_2\\dots":[10],"x_p$":[11],"of":[12,40,63,74],"distinct":[13],"vertices":[14,65],"such":[15,57],"that":[16,58,93,116],"either":[17],"$x_ix_{i+1}\\in":[18,30],"A$":[19,22,31],"or":[20,23],"$x_{i+1}x_{i}\\in":[21],"both":[24],"for":[25],"every":[26,94,117,136],"$i\\in":[27],"[p-1]$.":[28],"If":[29],"in":[32],"$P$,":[33],"then":[34],"$x_ix_{i+1}$":[35],"forward":[38],"arc":[39,70],"$P$;":[41],"otherwise,":[42],"$x_{i+1}x_{i}$":[43],"backward":[46,112,133,152],"arc.":[47],"The":[48],"independence":[49],"number":[50],"$\u03b1(D)$":[51],"the":[53],"maximum":[54],"integer":[55],"$p$":[56,64],"$D$":[59,120,139],"has":[60,103,124,143],"set":[62],"where":[66],"there":[67],"no":[69],"between":[71],"any":[72],"pair":[73],"vertices.":[75],"A":[76],"$k$-connected":[79],"if":[80],"its":[81],"underlying":[82],"undirected":[83],"graph":[84,97],"$k$-connected.":[86],"Freschi":[87],"and":[88,135],"Lo":[89],"(JCT-B":[90],"2024)":[91],"proved":[92],"$n$-vertex":[95],"with":[98,108,121,129,140,148],"minimum":[99],"degree":[100],"$\u03b4\\ge":[101],"n/2$":[102],"Hamilton":[105,126,145],"cycle":[107,128],"at":[109,130,149],"most":[110,131,150],"$n-\u03b4$":[111],"arcs.":[113,153],"We":[114],"prove":[115],"2-connected":[118],"$\u03b1(D)\\le":[122,141],"2$":[123,142],"five":[132],"arcs,":[134],"1-connected":[137],"two":[151]},"counts_by_year":[],"updated_date":"2026-03-26T06:10:45.909354","created_date":"2026-03-26T00:00:00"}