{"id":"https://openalex.org/W4396954125","doi":"https://doi.org/10.1007/s00454-024-00649-7","title":"Annulus Graphs in $$\\mathbb R^d$$","display_name":"Annulus Graphs in $$\\mathbb R^d$$","publication_year":2024,"publication_date":"2024-05-16","ids":{"openalex":"https://openalex.org/W4396954125","doi":"https://doi.org/10.1007/s00454-024-00649-7"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-024-00649-7","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00454-024-00649-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-024-00649-7.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-024-00649-7.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035246279","display_name":"Lyuben Lichev","orcid":"https://orcid.org/0000-0002-3998-8920"},"institutions":[{"id":"https://openalex.org/I24768866","display_name":"Bulgarian Academy of Sciences","ror":"https://ror.org/01x8hew03","country_code":"BG","type":"government","lineage":["https://openalex.org/I24768866"]},{"id":"https://openalex.org/I4210105926","display_name":"Institute of Mathematics and Informatics","ror":"https://ror.org/01b5dy719","country_code":"BG","type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4210105926"]},{"id":"https://openalex.org/I86767153","display_name":"Universit\u00e9 Jean Monnet","ror":"https://ror.org/04yznqr36","country_code":"FR","type":"education","lineage":["https://openalex.org/I86767153"]}],"countries":["BG","FR"],"is_corresponding":false,"raw_author_name":"Lyuben Lichev","raw_affiliation_strings":["Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria","Universit\u00e9 Jean Monnet, Saint-\u00c9tienne, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria","institution_ids":["https://openalex.org/I4210105926","https://openalex.org/I24768866"]},{"raw_affiliation_string":"Universit\u00e9 Jean Monnet, Saint-\u00c9tienne, France","institution_ids":["https://openalex.org/I86767153"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083558993","display_name":"Tsvetomir Mihaylov","orcid":"https://orcid.org/0000-0002-7363-7139"},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Tsvetomir Mihaylov","raw_affiliation_strings":["University of Birmingham, Birmingham, UK"],"raw_orcid":"https://orcid.org/0000-0002-7363-7139","affiliations":[{"raw_affiliation_string":"University of Birmingham, Birmingham, UK","institution_ids":["https://openalex.org/I79619799"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5083558993"],"corresponding_institution_ids":["https://openalex.org/I79619799"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08408963,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"72","issue":"1","first_page":"379","last_page":"401"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/annulus","display_name":"Annulus (botany)","score":0.5937445163726807},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.44738060235977173},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3921802043914795},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.37834715843200684},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3634622097015381},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3210331201553345},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.19906851649284363},{"id":"https://openalex.org/keywords/composite-material","display_name":"Composite material","score":0.06059819459915161}],"concepts":[{"id":"https://openalex.org/C150936888","wikidata":"https://www.wikidata.org/wiki/Q4769748","display_name":"Annulus (botany)","level":2,"score":0.5937445163726807},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44738060235977173},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3921802043914795},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.37834715843200684},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3634622097015381},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3210331201553345},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.19906851649284363},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.06059819459915161}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00454-024-00649-7","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00454-024-00649-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-024-00649-7.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:publications/a6de8861-85a0-462c-8fa7-de6a81fb2aca","is_oa":true,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/a6de8861-85a0-462c-8fa7-de6a81fb2aca","pdf_url":"https://pure-oai.bham.ac.uk/ws/files/228500896/454_2024_Article_649.pdf","source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"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":"Lichev , L & Mihaylov , T 2024 , ' Annulus Graphs in R d ' , Discrete & Computational Geometry , vol. 72 , no. 1 , pp. 379-401 . https://doi.org/10.1007/s00454-024-00649-7","raw_type":"article"},{"id":"pmh:oai:HAL:hal-04992207v1","is_oa":false,"landing_page_url":"https://hal.science/hal-04992207","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Discrete and Computational Geometry, 2024, 72 (1), pp.379-401. &#x27E8;10.1007/s00454-024-00649-7&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"doi:10.1007/s00454-024-00649-7","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00454-024-00649-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-024-00649-7.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4396954125.pdf"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W13621767","https://openalex.org/W102543617","https://openalex.org/W630423399","https://openalex.org/W1565715892","https://openalex.org/W1716595998","https://openalex.org/W1965907328","https://openalex.org/W1984912602","https://openalex.org/W2003364078","https://openalex.org/W2019029270","https://openalex.org/W2049267709","https://openalex.org/W2057256606","https://openalex.org/W2064197162","https://openalex.org/W2082052321","https://openalex.org/W2088521668","https://openalex.org/W2105808107","https://openalex.org/W2106745795","https://openalex.org/W2112541047","https://openalex.org/W2139349113","https://openalex.org/W2254751494","https://openalex.org/W2321124713","https://openalex.org/W2477674116","https://openalex.org/W2963183679","https://openalex.org/W2971629382","https://openalex.org/W2980367889","https://openalex.org/W3080973359","https://openalex.org/W3099777322","https://openalex.org/W4210453869","https://openalex.org/W4255063253"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2379021478","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W1990384283","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2038876018","https://openalex.org/W2142036596"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"d":[2,137],"-dimensional":[3,138],"annulus":[4,139],"graph":[5,48],"with":[6,141],"radii":[7,142],"$$R_1$$":[8,143],"<mml:math":[9,18,29,53,87,114,144,153,165,199,232,279,294,313,334],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[10,19,30,54,88,115,145,154,166,200,233,280,295,314,335],"<mml:msub>":[11,20,32,37,91,96,117,123,128,146,155,168,173,202,208,213,235,240,246,251,297,302,316,321],"<mml:mi>R</mml:mi>":[12,21,33,38,56,92,97,124,129,147,156,169,174,209,214,247,252,298,303,317,322],"<mml:mn>1</mml:mn>":[13,39,93,125,148,175,210,248,299,323],"</mml:msub>":[14,23,35,40,94,99,120,126,131,149,158,171,176,205,211,216,243,249,254,258,300,305,319,324],"</mml:math>":[15,24,44,59,102,135,150,159,178,220,273,290,307,328],"and":[16,65,71,151,329],"$$R_2$$":[17,152],"<mml:mn>2</mml:mn>":[22,34,98,130,157,170,215,253,304,318],"(here":[25],"$$R_2\\ge":[26,309],"R_1\\ge":[27],"0$$":[28,312],"<mml:mrow>":[31,89,116,121,167,201,206,234,237,244,260,267,281,296,315,336],"<mml:mo>\u2265</mml:mo>":[36,41,320],"<mml:mn>0</mml:mn>":[42,326],"</mml:mrow>":[43,101,133,134,177,218,219,256,257,264,271,272,289,306,327],")":[45],"is":[46,160,182,274],"a":[47,187,190],"embeddable":[49],"in":[50,76,82],"$$\\mathbb":[51],"R^d$$":[52],"<mml:msup>":[55],"<mml:mi>d</mml:mi>":[57,119,204,242,286],"</mml:msup>":[58],"so":[60],"that":[61,109,224],"two":[62],"vertices":[63],"u":[64],"v":[66],"form":[67],"an":[68],"edge":[69],"if":[70,73],"only":[72],"their":[74],"images":[75],"the":[77,83,110,194],"embedding":[78],"are":[79],"at":[80],"distance":[81],"interval":[84],"$$[R_1,":[85],"R_2]$$":[86],"<mml:mo>[</mml:mo>":[90],"<mml:mo>,</mml:mo>":[95,127,212,250,301],"<mml:mo>]</mml:mo>":[100],".":[103],"In":[104],"this":[105,180],"paper":[106],"we":[107,222],"show":[108,223],"family":[111],"$$\\mathcal":[112,197],"A_d(R_1,R_2)$$":[113,198],"<mml:mi>A</mml:mi>":[118,203,241],"<mml:mo>(</mml:mo>":[122,207,245,261,268,283,285],"<mml:mo>)</mml:mo>":[132,217,255,263,270,287,288],"of":[136,193,196],"graphs":[140],"uniquely":[161],"characterised":[162],"by":[163,276],"$$R_2/R_1$$":[164],"<mml:mo>/</mml:mo>":[172,265],"when":[179],"ratio":[181],"sufficiently":[183],"large.":[184],"Moreover,":[185],"as":[186],"step":[188],"towards":[189],"better":[191],"understanding":[192],"structure":[195],",":[221],"$$\\sup":[225],"_{G\\in":[226],"\\mathcal":[227],"A_d(R_1,R_2)}":[228],"\\chi":[229],"(G)/\\omega":[230],"(G)$$":[231],"<mml:mo>sup</mml:mo>":[236],"<mml:mi>G</mml:mi>":[238,262,269],"<mml:mo>\u2208</mml:mo>":[239],"<mml:mi>\u03c7</mml:mi>":[259],"<mml:mi>\u03c9</mml:mi>":[266],"given":[275],"$$\\exp":[277,331],"(O(d))$$":[278],"<mml:mo>exp</mml:mo>":[282,337],"<mml:mi>O</mml:mi>":[284],"for":[291],"all":[292],"$$R_1,R_2$$":[293],"satisfying":[308],"R_1":[310],"&gt;":[311],"<mml:mo>&gt;</mml:mo>":[325],"also":[330],"(\\Omega":[332],"(d))$$":[333]},"counts_by_year":[],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}