{"id":"https://openalex.org/W7118452869","doi":"https://doi.org/10.48550/arxiv.2601.00957","title":"Algorithmic Applications of Tyshkevich's Graph Decomposition: A Primer and a Toolkit","display_name":"Algorithmic Applications of Tyshkevich's Graph Decomposition: A Primer and a Toolkit","publication_year":2026,"publication_date":"2026-01-02","ids":{"openalex":"https://openalex.org/W7118452869","doi":"https://doi.org/10.48550/arxiv.2601.00957"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2601.00957","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.00957","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.2601.00957","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101427454","display_name":"Christine T. Cheng","orcid":"https://orcid.org/0000-0003-0524-5368"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cheng, Christine T.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5122144652","display_name":"Chelsea Ann Lambert","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lambert, Chelsea Ann","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"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/T11435","display_name":"Polynomial and algebraic computation","score":0.4237000048160553,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.4237000048160553,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.17239999771118164,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.09459999948740005,"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/graph","display_name":"Graph","score":0.567799985408783},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.45419999957084656},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4277999997138977},{"id":"https://openalex.org/keywords/graph-algorithms","display_name":"Graph algorithms","score":0.41850000619888306},{"id":"https://openalex.org/keywords/graph-rewriting","display_name":"Graph rewriting","score":0.3935999870300293},{"id":"https://openalex.org/keywords/wait-for-graph","display_name":"Wait-for graph","score":0.36079999804496765},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.3368000090122223}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6680999994277954},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.567799985408783},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5582000017166138},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.45419999957084656},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4277999997138977},{"id":"https://openalex.org/C2986651925","wikidata":"https://www.wikidata.org/wiki/Q1514868","display_name":"Graph algorithms","level":3,"score":0.41850000619888306},{"id":"https://openalex.org/C558772884","wikidata":"https://www.wikidata.org/wiki/Q1508564","display_name":"Graph rewriting","level":3,"score":0.3935999870300293},{"id":"https://openalex.org/C106891557","wikidata":"https://www.wikidata.org/wiki/Q4148051","display_name":"Wait-for graph","level":4,"score":0.36079999804496765},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.3368000090122223},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3176000118255615},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31119999289512634},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.3000999987125397},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2856999933719635},{"id":"https://openalex.org/C64339825","wikidata":"https://www.wikidata.org/wiki/Q722659","display_name":"Graph property","level":5,"score":0.2727000117301941},{"id":"https://openalex.org/C5737132","wikidata":"https://www.wikidata.org/wiki/Q1101814","display_name":"Clique-width","level":5,"score":0.26899999380111694},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2621999979019165},{"id":"https://openalex.org/C176225458","wikidata":"https://www.wikidata.org/wiki/Q595971","display_name":"Graph database","level":3,"score":0.257099986076355},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.25380000472068787},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.25380000472068787},{"id":"https://openalex.org/C17169500","wikidata":"https://www.wikidata.org/wiki/Q3033506","display_name":"Null graph","level":5,"score":0.2502000033855438}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2601.00957","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.00957","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.2601.00957","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.00957","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":{"A":[0],"graph":[1,41,84],"that":[2,37,97],"is":[3,10,65],"completely":[4],"determined":[5],"by":[6],"its":[7],"degree":[8],"sequence":[9,47],"called":[11],"a":[12,34,46,52,94],"unigraph.":[13],"In":[14],"2000,":[15],"Regina":[16],"Tyshkevich":[17],"published":[18],"one":[19],"of":[20,48,55,72,82,86],"the":[21,32,80,99],"most":[22],"important":[23],"papers":[24],"on":[25],"unigraphs.":[26,58],"There":[27],"are":[28],"two":[29],"parts":[30],"to":[31],"paper:":[33],"decomposition":[35],"theorem":[36],"describes":[38],"how":[39,62,77],"every":[40,63],"can":[42],"be":[43],"broken":[44],"into":[45],"basic":[49,57],"graphs":[50],"and":[51,75],"complete":[53],"classification":[54],"all":[56],"Together,":[59],"they":[60,78],"reveal":[61],"unigraph":[64],"constructed.":[66],"We":[67,91],"provide":[68],"an":[69],"informal":[70],"overview":[71],"Tyshkevich's":[73],"results":[74],"show":[76],"enable":[79],"computation":[81],"various":[83],"parameters":[85],"unigraphs":[87],"in":[88,102],"linear":[89],"time.":[90],"also":[92],"created":[93],"toolkit":[95],"(https://chelseal11.github.io/tyshkevich_decomposition_toolkit/)":[96],"implements":[98],"algorithms":[100],"described":[101],"this":[103],"write-up.":[104]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-01-08T00:00:00"}
