{"id":"https://openalex.org/W4239751875","doi":"https://doi.org/10.1002/(sici)1097-0118(199712)26:4<195::aid-jgt3>3.0.co;2-l","title":"Bandwidth edge counts for linear arrangements of rectangular grids","display_name":"Bandwidth edge counts for linear arrangements of rectangular grids","publication_year":1997,"publication_date":"1997-12-01","ids":{"openalex":"https://openalex.org/W4239751875","doi":"https://doi.org/10.1002/(sici)1097-0118(199712)26:4<195::aid-jgt3>3.0.co;2-l"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1097-0118(199712)26:4<195::aid-jgt3>3.0.co;2-l","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(199712)26:4<195::aid-jgt3>3.0.co;2-l","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/A5109079434","display_name":"Peter C. Fishburn","orcid":null},"institutions":[{"id":"https://openalex.org/I1283103587","display_name":"AT&T (United States)","ror":"https://ror.org/02bbd5539","country_code":"US","type":"company","lineage":["https://openalex.org/I1283103587"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Peter Fishburn","raw_affiliation_strings":["AT&T Labs\u2013Research, Florham Park, NJ 07932"],"affiliations":[{"raw_affiliation_string":"AT&T Labs\u2013Research, Florham Park, NJ 07932","institution_ids":["https://openalex.org/I1283103587"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102817905","display_name":"Paul Wright","orcid":"https://orcid.org/0000-0001-5297-6257"},"institutions":[{"id":"https://openalex.org/I1283103587","display_name":"AT&T (United States)","ror":"https://ror.org/02bbd5539","country_code":"US","type":"company","lineage":["https://openalex.org/I1283103587"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Paul Wright","raw_affiliation_strings":["AT&T Labs\u2013Research, Florham Park, NJ 07932"],"affiliations":[{"raw_affiliation_string":"AT&T Labs\u2013Research, Florham Park, NJ 07932","institution_ids":["https://openalex.org/I1283103587"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5109079434"],"corresponding_institution_ids":["https://openalex.org/I1283103587"],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.39521814,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"26","issue":"4","first_page":"195","last_page":"202"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9983000159263611,"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"}},{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9973999857902527,"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":0.8454766273498535},{"id":"https://openalex.org/keywords/lexicographical-order","display_name":"Lexicographical order","score":0.8248975276947021},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8231328725814819},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.6074480414390564},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5925517082214355},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5906316041946411},{"id":"https://openalex.org/keywords/row","display_name":"Row","score":0.4924374520778656},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4721237123012543},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37641024589538574},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.24910694360733032},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09358733892440796}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8454766273498535},{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.8248975276947021},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8231328725814819},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.6074480414390564},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5925517082214355},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5906316041946411},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.4924374520778656},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4721237123012543},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37641024589538574},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.24910694360733032},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09358733892440796},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/(sici)1097-0118(199712)26:4<195::aid-jgt3>3.0.co;2-l","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(199712)26:4<195::aid-jgt3>3.0.co;2-l","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":[{"score":0.5400000214576721,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1993634787","https://openalex.org/W3125614403","https://openalex.org/W2476923378","https://openalex.org/W2803221307","https://openalex.org/W2951826204","https://openalex.org/W4211001408","https://openalex.org/W4312734339","https://openalex.org/W2964314221","https://openalex.org/W4301521638","https://openalex.org/W2269982198"],"abstract_inverted_index":{"Let":[0],"Gn,m":[1,38,62],"denote":[2],"a":[3,52,95,106],"graph":[4],"with":[5,18],"nm":[6],"vertices":[7,24],"arranged":[8],"in":[9,51],"n":[10,73],"rows":[11],"and":[12,26],"m":[13],"\u2265":[14],"max{n,":[15],"2}":[16],"columns":[17],"an":[19],"edge":[20],"{u,":[21],"v}":[22],"between":[23],"u":[25],"v":[27],"if":[28],"they":[29],"are":[30],"adjacent":[31],"horizontally":[32],"or":[33],"vertically.":[34],"The":[35,89],"bandwidth":[36],"of":[37,49,61],"is":[39,92,103],"known":[40],"to":[41,85],"equal":[42],"n.":[43],"We":[44],"prove":[45],"that":[46],"the":[47,58,100],"number":[48],"edges":[50],"bandwidth-achieving":[53],"linear":[54,98,109],"arrangement":[55],"f":[56],"from":[57,76],"vertex":[59],"set":[60],"onto":[63],"{1,":[64],"2,\u2026,":[65],"nm}":[66],"for":[67,94],"which":[68],"|f(u)":[69],"-":[70,78,82,87],"f(v)|":[71],"=":[72],"can":[74],"range":[75],"2(n":[77],"1)":[79],"+":[80],"n(m":[81,86],"n)":[83],"up":[84],"1).":[88],"lower":[90],"bound":[91,102],"attained":[93,104],"down-diagonal":[96],"lexicographic":[97,108],"arrangement;":[99],"upper":[101],"by":[105],"column-row":[107],"arrangement.":[110],"\u00a9":[111],"1997":[112,123],"John":[113],"Wiley":[114],"&":[115],"Sons,":[116],"Inc.":[117],"J":[118],"Graph":[119],"Theory":[120],"26:":[121],"195\u2013202,":[122]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
