{"id":"https://openalex.org/W7127190781","doi":"https://doi.org/10.48550/arxiv.2601.23198","title":"Planar Graph Homomorphisms: A Dichotomy and a Barrier from Quantum Groups","display_name":"Planar Graph Homomorphisms: A Dichotomy and a Barrier from Quantum Groups","publication_year":2026,"publication_date":"2026-01-30","ids":{"openalex":"https://openalex.org/W7127190781","doi":"https://doi.org/10.48550/arxiv.2601.23198"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2601.23198","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101599971","display_name":"Jin\u2010Yi Cai","orcid":"https://orcid.org/0009-0003-0675-6060"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cai, Jin-Yi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124863848","display_name":"Ashwin Maran","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Maran, Ashwin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5042102052","display_name":"Ben Young","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Young, Ben","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.125507,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.37380000948905945,"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"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.37380000948905945,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.17080000042915344,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.1573999971151352,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/planar","display_name":"Planar","score":0.6015999913215637},{"id":"https://openalex.org/keywords/homomorphism","display_name":"Homomorphism","score":0.5511000156402588},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.5465999841690063},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4909000098705292},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.48089998960494995},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.4499000012874603},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4108999967575073},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.3402000069618225}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7175999879837036},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6015999913215637},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.5511000156402588},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.5465999841690063},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5432000160217285},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4909000098705292},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.48089998960494995},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4684000015258789},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.4499000012874603},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4108999967575073},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.3402000069618225},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.3346000015735626},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.32760000228881836},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.31679999828338623},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.30320000648498535},{"id":"https://openalex.org/C131930043","wikidata":"https://www.wikidata.org/wiki/Q7200964","display_name":"Planar straight-line graph","level":5,"score":0.2985000014305115},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.27300000190734863},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26159998774528503},{"id":"https://openalex.org/C84392682","wikidata":"https://www.wikidata.org/wiki/Q1952404","display_name":"Multilinear map","level":2,"score":0.26080000400543213},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2601.23198","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2601.23198","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.23198","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2601.23198","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"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":"submittedVersion","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":{"We":[0,90,115],"study":[1],"the":[2,58,79,83,93,107,110,137,149,166],"complexity":[3,76],"of":[4,57,86,95,109,126,139],"counting":[5,154],"(weighted)":[6],"planar":[7,68,80,87,118,152,167],"graph":[8,59],"homomorphism":[9,153],"problem":[10,138],"$\\tt{Pl\\text{-}GH}(M)$":[11,35],"parametrized":[12],"by":[13,61],"an":[14],"arbitrary":[15],"symmetric":[16],"non-negative":[17],"real":[18],"valued":[19],"matrix":[20],"$M$.":[21],"For":[22],"matrices":[23],"with":[24],"pairwise":[25],"distinct":[26],"diagonal":[27],"values,":[28],"we":[29,49],"prove":[30,135],"a":[31,44,51],"complete":[32],"dichotomy":[33,52],"theorem:":[34],"is":[36,82,132,142,144],"either":[37],"polynomial-time":[38],"tractable,":[39],"or":[40],"$\\#$P-hard,":[41],"according":[42],"to":[43,99,160,165],"simple":[45],"criterion.":[46],"More":[47],"generally,":[48],"obtain":[50],"whenever":[53],"every":[54],"vertex":[55,124],"pair":[56],"represented":[60],"$M$":[62,127],"can":[63,122],"be":[64],"separated":[65],"using":[66],"some":[67],"edge":[69,88,104,119],"gadget.":[70],"A":[71],"key":[72],"question":[73],"in":[74,78],"proving":[75],"dichotomies":[77],"setting":[81],"expressive":[84],"power":[85],"gadgets.":[89],"build":[91],"on":[92],"framework":[94],"Man\u010dinska":[96],"and":[97,106,134,156],"Roberson":[98],"establish":[100],"links":[101],"between":[102],"\\textit{planar}":[103],"gadgets":[105,120],"theory":[108],"\\textit{quantum":[111],"automorphism":[112],"group}":[113],"$\\tt{Qut}(M)$.":[114],"show":[116],"that":[117,121,136],"separate":[123],"pairs":[125],"exist":[128],"precisely":[129],"when":[130],"$\\tt{Qut}(M)$":[131,141],"\\emph{trivial},":[133],"whether":[140],"trivial":[143],"undecidable.":[145],"These":[146],"results":[147],"delineate":[148],"frontier":[150],"for":[151],"problems":[155],"uncover":[157],"intrinsic":[158],"barriers":[159],"extending":[161],"nonplanar":[162],"reduction":[163],"techniques":[164],"setting.":[168]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-02-03T00:00:00"}
