{"id":"https://openalex.org/W2129094712","doi":"https://doi.org/10.1002/jgt.3190060211","title":"A shortness exponent for <i>r</i>\u2010regular <i>r</i>\u2010connected graphs","display_name":"A shortness exponent for <i>r</i>\u2010regular <i>r</i>\u2010connected graphs","publication_year":1982,"publication_date":"1982-06-01","ids":{"openalex":"https://openalex.org/W2129094712","doi":"https://doi.org/10.1002/jgt.3190060211","mag":"2129094712"},"language":"en","primary_location":{"id":"doi:10.1002/jgt.3190060211","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190060211","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109206727","display_name":"Brad Jackson","orcid":null},"institutions":[{"id":"https://openalex.org/I185103710","display_name":"University of California, Santa Cruz","ror":"https://ror.org/03s65by71","country_code":"US","type":"education","lineage":["https://openalex.org/I185103710"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Brad Jackson","raw_affiliation_strings":["University of California Santa Cruz, Ca 95064","University of California, Santa Cruz, CA 95064#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California Santa Cruz, Ca 95064","institution_ids":["https://openalex.org/I185103710"]},{"raw_affiliation_string":"University of California, Santa Cruz, CA 95064#TAB#","institution_ids":["https://openalex.org/I185103710"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065606883","display_name":"T. D. Parsons","orcid":null},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"T. D. Parsons","raw_affiliation_strings":["Pennsylvania State University University Park, Pa 16802","Pennsylvania State University\u2028University Park, PA 16802"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Pennsylvania State University University Park, Pa 16802","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"Pennsylvania State University\u2028University Park, PA 16802","institution_ids":["https://openalex.org/I130769515"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":0.6815,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.70971039,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"6","issue":"2","first_page":"169","last_page":"176"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9998000264167786,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8779159784317017},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8721548318862915},{"id":"https://openalex.org/keywords/valency","display_name":"Valency","score":0.8612722158432007},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6104527711868286},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.608906626701355},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5435017347335815},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42237389087677}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8779159784317017},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8721548318862915},{"id":"https://openalex.org/C139007053","wikidata":"https://www.wikidata.org/wiki/Q1412952","display_name":"Valency","level":2,"score":0.8612722158432007},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6104527711868286},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.608906626701355},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5435017347335815},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42237389087677},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/jgt.3190060211","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190060211","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1973490548","https://openalex.org/W2013151284","https://openalex.org/W2027269133","https://openalex.org/W2125993726","https://openalex.org/W2140953172","https://openalex.org/W2327953950","https://openalex.org/W2977998329","https://openalex.org/W6653730139"],"related_works":["https://openalex.org/W431658849","https://openalex.org/W2762663192","https://openalex.org/W1992814711","https://openalex.org/W638739646","https://openalex.org/W4212917371","https://openalex.org/W1998523619","https://openalex.org/W1979918629","https://openalex.org/W2501908867","https://openalex.org/W2905041223","https://openalex.org/W4236936468"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"r":[2,16,40,51,57,63],"\u2267":[3,37,48],"3":[4],"be":[5],"an":[6,24,56],"integer.":[7],"It":[8],"is":[9,41,52,55],"shown":[10],"that":[11,33],"there":[12,54],"exists":[13],"\u03b5=":[14],"\u03b5(":[15],"),":[17],"0":[18,31],"&lt;":[19,21],"\u03b5":[20,75],"1,":[22],"and":[23],"integer":[25],"N":[26,38,49],"=":[27],"N(r":[28],")":[29],"&gt;":[30],"such":[32],"for":[34,44],"all":[35,45],"n":[36,47,66,74],"(if":[39,50],"even)":[42],"or":[43],"even":[46],"odd),":[53],"\u2010connected":[58],"regular":[59],"graph":[60],"of":[61],"valency":[62],"on":[64],"exactly":[65],"vertices":[67],"whose":[68],"longest":[69],"cycles":[70],"have":[71],"fewer":[72],"than":[73],"vertices.":[76]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}