{"id":"https://openalex.org/W7125489573","doi":"https://doi.org/10.48550/arxiv.2601.15890","title":"Existential Positive Transductions of Sparse Graphs","display_name":"Existential Positive Transductions of Sparse Graphs","publication_year":2026,"publication_date":"2026-01-22","ids":{"openalex":"https://openalex.org/W7125489573","doi":"https://doi.org/10.48550/arxiv.2601.15890"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2601.15890","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.15890","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.2601.15890","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000402695","display_name":"Nikolas M\u00e4hlmann","orcid":"https://orcid.org/0000-0003-3657-7736"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"M\u00e4hlmann, Nikolas","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Siebertz, Sebastian","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Siebertz, Sebastian","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5000402695"],"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":0.8112000226974487,"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":0.8112000226974487,"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":0.07660000026226044,"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/T10991","display_name":"Game Theory and Voting Systems","score":0.017500000074505806,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7939000129699707},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7717999815940857},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4456000030040741},{"id":"https://openalex.org/keywords/existentialism","display_name":"Existentialism","score":0.43470001220703125},{"id":"https://openalex.org/keywords/fragment","display_name":"Fragment (logic)","score":0.4212999939918518},{"id":"https://openalex.org/keywords/existential-quantification","display_name":"Existential quantification","score":0.41359999775886536},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.399399995803833},{"id":"https://openalex.org/keywords/graph-property","display_name":"Graph property","score":0.382999986410141}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7939000129699707},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7717999815940857},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5940999984741211},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5583000183105469},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5041999816894531},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4456000030040741},{"id":"https://openalex.org/C127882523","wikidata":"https://www.wikidata.org/wiki/Q38066","display_name":"Existentialism","level":2,"score":0.43470001220703125},{"id":"https://openalex.org/C2776235265","wikidata":"https://www.wikidata.org/wiki/Q18392052","display_name":"Fragment (logic)","level":2,"score":0.4212999939918518},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.41359999775886536},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.399399995803833},{"id":"https://openalex.org/C64339825","wikidata":"https://www.wikidata.org/wiki/Q722659","display_name":"Graph property","level":5,"score":0.382999986410141},{"id":"https://openalex.org/C195818886","wikidata":"https://www.wikidata.org/wiki/Q5421724","display_name":"Expressive power","level":2,"score":0.3711000084877014},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3240000009536743},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.30079999566078186},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2879999876022339},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2833999991416931},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2750999927520752},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.25519999861717224},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.2549000084400177}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2601.15890","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.15890","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.2601.15890","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.15890","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Monadic":[0],"stability":[1,194],"generalizes":[2],"many":[3],"tameness":[4],"notions":[5],"from":[6,108],"structural":[7],"graph":[8,30],"theory":[9],"such":[10,62],"as":[11,63,144,165,237],"planarity,":[12],"bounded":[13,15,67,76],"degree,":[14],"tree-width,":[16],"and":[17,69,80,202],"nowhere":[18,48,109],"density.":[19],"The":[20],"sparsification":[21,90],"conjecture":[22,54,121],"predicts":[23],"that":[24,35,93,104,163,225],"the":[25,45,71,87,94,119,134,141,147,166,171,180,189,199,217,233],"(possibly":[26],"dense)":[27],"monadically":[28,72,98],"stable":[29,73,99],"classes":[31,65,100,111],"are":[32,101],"exactly":[33,102],"those":[34,103],"can":[36,105],"be":[37,106],"logically":[38],"encoded":[39],"by":[40,195],"first-order":[41],"(FO)":[42],"transductions":[43],"in":[44,179],"(always":[46],"sparse)":[47],"dense":[49,110,148],"classes.":[50],"So":[51],"far":[52],"this":[53,83],"has":[55,232],"been":[56],"verified":[57],"for":[58,64,70,128,206],"several":[59],"special":[60,131],"cases,":[61],"of":[66,75,133,146,170,182,192,198],"shrub-depth,":[68],"fragments":[74],"(linear)":[77],"clique-width,":[78],"twin-width,":[79],"merge-width.":[81],"In":[82,209],"work":[84],"we":[85,124,139,155,187,222],"propose":[86],"existential":[88,114],"positive":[89,115,230,239],"conjecture,":[91],"predicting":[92],"more":[95,218],"restricted":[96],"co-matching-free,":[97],"transduced":[107],"using":[112],"only":[113],"FO":[116],"formulas.":[117],"While":[118],"general":[120],"remains":[122],"open,":[123],"verify":[125],"its":[126],"truth":[127],"all":[129],"known":[130,200],"cases":[132],"original":[135],"conjecture.":[136],"Even":[137],"stronger,":[138],"find":[140],"sparse":[142],"preimages":[143],"subgraphs":[145],"input":[149],"graphs.":[150],"As":[151],"a":[152,157,176],"key":[153],"ingredient,":[154],"introduce":[156],"new":[158],"combinatorial":[159],"operation,":[160,173],"called":[161],"subflip,":[162],"arises":[164],"natural":[167],"co-matching-free":[168,190],"analog":[169],"flip":[172],"which":[174],"is":[175],"central":[177],"tool":[178],"characterization":[181],"monadic":[183,193,207],"stability.":[184,208],"Using":[185],"subflips,":[186],"characterize":[188],"fragment":[191],"appropriate":[196],"strengthenings":[197],"flip-flatness":[201],"flipper":[203],"game":[204],"characterizations":[205],"an":[210],"attempt":[211],"to":[212,216],"generalize":[213],"our":[214],"results":[215],"expressive":[219,235],"MSO":[220,231],"logic,":[221],"discover":[223],"(rediscover?)":[224],"on":[226],"relational":[227],"structures":[228],"(existential)":[229,238],"same":[234],"power":[236],"FO.":[240]},"counts_by_year":[],"updated_date":"2026-03-25T23:56:10.502304","created_date":"2026-01-24T00:00:00"}
