{"id":"https://openalex.org/W4415270608","doi":"https://doi.org/10.48550/arxiv.2510.12544","title":"Unimodular toric ideals of graphs","display_name":"Unimodular toric ideals of graphs","publication_year":2025,"publication_date":"2025-10-14","ids":{"openalex":"https://openalex.org/W4415270608","doi":"https://doi.org/10.48550/arxiv.2510.12544"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2510.12544","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.12544","pdf_url":"https://arxiv.org/pdf/2510.12544","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2510.12544","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001467912","display_name":"Christos Tatakis","orcid":"https://orcid.org/0000-0002-0112-6313"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tatakis, Christos","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5001467912"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11476","display_name":"Graph theory and applications","score":0.9546999931335449,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9495999813079834,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/unimodular-matrix","display_name":"Unimodular matrix","score":0.9549999833106995},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.5091999769210815},{"id":"https://openalex.org/keywords/incidence-matrix","display_name":"Incidence matrix","score":0.5002999901771545},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.47600001096725464},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.3686000108718872},{"id":"https://openalex.org/keywords/graph-theory","display_name":"Graph theory","score":0.3019999861717224}],"concepts":[{"id":"https://openalex.org/C201958917","wikidata":"https://www.wikidata.org/wiki/Q1367055","display_name":"Unimodular matrix","level":2,"score":0.9549999833106995},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6902999877929688},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6190000176429749},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.5091999769210815},{"id":"https://openalex.org/C85136909","wikidata":"https://www.wikidata.org/wiki/Q939272","display_name":"Incidence matrix","level":3,"score":0.5002999901771545},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.47600001096725464},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39959999918937683},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3686000108718872},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.3019999861717224},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.2833000123500824},{"id":"https://openalex.org/C61511704","wikidata":"https://www.wikidata.org/wiki/Q1671857","display_name":"Incidence (geometry)","level":2,"score":0.25690001249313354},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.25360000133514404}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2510.12544","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.12544","pdf_url":"https://arxiv.org/pdf/2510.12544","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2510.12544","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2510.12544","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2510.12544","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.12544","pdf_url":"https://arxiv.org/pdf/2510.12544","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415270608.pdf","grobid_xml":"https://content.openalex.org/works/W4415270608.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"give":[1],"a":[2,17,34],"necessary":[3],"and":[4,40],"sufficient":[5],"graph-theoretic":[6],"characterization":[7],"of":[8,11,24,33,47],"toric":[9],"ideals":[10],"graphs":[12,26],"that":[13,29],"are":[14],"unimodular.":[15],"As":[16],"direct":[18],"consequence,":[19],"we":[20],"provide":[21],"the":[22,30],"structure":[23],"unimodular":[25,38],"by":[27],"proving":[28],"incidence":[31],"matrix":[32],"graph":[35],"$G$":[36,48],"is":[37],"if":[39,42],"only":[41],"any":[43],"two":[44],"odd":[45],"cycles":[46],"intersect.":[49]},"counts_by_year":[],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-10-17T00:00:00"}