{"id":"https://openalex.org/W2963607195","doi":"https://doi.org/10.37236/7942","title":"Clumsy Packings of Graphs","display_name":"Clumsy Packings of Graphs","publication_year":2019,"publication_date":"2019-06-21","ids":{"openalex":"https://openalex.org/W2963607195","doi":"https://doi.org/10.37236/7942","mag":"2963607195"},"language":"en","primary_location":{"id":"doi:10.37236/7942","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7942","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i2p39/7854","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i2p39/7854","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079004436","display_name":"Maria Axenovich","orcid":"https://orcid.org/0000-0002-8843-9557"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Maria Axenovich","raw_affiliation_strings":["Karlsruhe Institute of Technology"],"affiliations":[{"raw_affiliation_string":"Karlsruhe Institute of Technology","institution_ids":["https://openalex.org/I102335020"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058670910","display_name":"Anika Kaufmann","orcid":null},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Anika Kaufmann","raw_affiliation_strings":["Karlsruhe Institute of Technology"],"affiliations":[{"raw_affiliation_string":"Karlsruhe Institute of Technology","institution_ids":["https://openalex.org/I102335020"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026016357","display_name":"Raphael Yuster","orcid":"https://orcid.org/0000-0001-7550-6506"},"institutions":[{"id":"https://openalex.org/I91203450","display_name":"University of Haifa","ror":"https://ror.org/02f009v59","country_code":"IL","type":"education","lineage":["https://openalex.org/I91203450"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Raphael Yuster","raw_affiliation_strings":["University of Haifa"],"affiliations":[{"raw_affiliation_string":"University of Haifa","institution_ids":["https://openalex.org/I91203450"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5079004436"],"corresponding_institution_ids":["https://openalex.org/I102335020"],"apc_list":null,"apc_paid":null,"fwci":0.7759,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.74546854,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":96},"biblio":{"volume":"26","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9872999787330627,"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":0.9872999787330627,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9747999906539917,"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"}},{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9607999920845032,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/combinatorics","display_name":"Combinatorics","score":0.895478367805481},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.6190876364707947},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.588860273361206},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5055892467498779},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.4741593897342682},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3231687545776367},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06691831350326538}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.895478367805481},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6190876364707947},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.588860273361206},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5055892467498779},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.4741593897342682},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3231687545776367},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06691831350326538},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/7942","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7942","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i2p39/7854","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/7942","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7942","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i2p39/7854","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2963607195.pdf","grobid_xml":"https://content.openalex.org/works/W2963607195.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1504418244","https://openalex.org/W1636454816","https://openalex.org/W1971289435","https://openalex.org/W1977424097","https://openalex.org/W1994941667","https://openalex.org/W2002540991","https://openalex.org/W2006263883","https://openalex.org/W2051660589","https://openalex.org/W2091476183","https://openalex.org/W2155295958","https://openalex.org/W2555546311","https://openalex.org/W2962716898","https://openalex.org/W6628667382","https://openalex.org/W6639073598","https://openalex.org/W6644757543","https://openalex.org/W6663139825","https://openalex.org/W6779915889"],"related_works":["https://openalex.org/W1971174658","https://openalex.org/W2002177687","https://openalex.org/W2099195351","https://openalex.org/W132109778","https://openalex.org/W1989984537","https://openalex.org/W2499670206","https://openalex.org/W24519920","https://openalex.org/W4253000595","https://openalex.org/W2087778462","https://openalex.org/W1553466895"],"abstract_inverted_index":{"Let":[0,77],"$G$":[1,14,39,169,176],"and":[2,94,123],"$H$":[3,24,167],"be":[4,79],"graphs.":[5],"We":[6,88,126],"say":[7],"that":[8,40,140,159],"$P$":[9,16,29,66],"is":[10,17,30,34,67,72,147,157,160],"an":[11,179],"$H$-packing":[12,28,37,65,85],"of":[13,20,23,38,45,74,82,86,105,151,164,166,187],"if":[15,32,70],"a":[18,83],"set":[19],"edge-disjoint":[21],"copies":[22,165],"in":[25,95,168,178],"$G$.":[26,87],"An":[27,64],"maximal":[31,62,73],"there":[33],"no":[35],"other":[36],"properly":[41],"contains":[42],"P.":[43],"Packings":[44],"maximum":[46],"cardinality":[47,61],"have":[48],"been":[49],"studied":[50],"intensively,":[51],"with":[52],"several":[53],"recent":[54],"breakthrough":[55],"results.":[56],"Here,":[57],"we":[58,138],"consider":[59],"minimum":[60,75],"packings.":[63],"called":[68],"clumsy":[69,84],"it":[71],"size.":[76],"$\\mathrm{cl}(G,H)$":[78,100,192],"the":[80,148,161],"size":[81],"provide":[89],"nontrivial":[90],"bounds":[91,190],"for":[92,101,130,191],"$\\mathrm{cl}(G,H)$,":[93],"many":[96],"cases":[97],"asymptotically":[98,127],"determine":[99,128],"some":[102],"generic":[103],"classes":[104],"graphs":[106],"G":[107],"such":[108],"as":[109,118,120,196],"$K_n$":[110],"(the":[111,115],"complete":[112],"graph),":[113,117],"$Q_n$":[114],"cube":[116],"well":[119],"square,":[121],"triangular,":[122],"hexagonal":[124],"grids.":[125],"$\\mathrm{cl}(K_n,H)$":[129],"every":[131],"fixed":[132],"non-empty":[133],"graph":[134],"$H$.":[135,152],"In":[136],"particular,":[137],"prove":[139],"$$\\mathrm{cl}(K_n,":[141],"H)":[142],"=":[143],"\\frac{\\binom{n}{2}-":[144],"\\mathrm{ex}(n,H)}{|E(H)|}+o(\\mathrm{ex}(n,H)),$$where":[145],"$ex(n,H)$":[146],"extremal":[149],"number":[150,163],"A":[153],"related":[154],"natural":[155],"parameter":[156],"$\\mathrm{cov}(G,H)$,":[158],"smallest":[162],"(not":[170],"necessarily":[171],"edge-disjoint)":[172],"whose":[173],"removal":[174],"from":[175],"results":[177],"$H$-free":[180],"graph.":[181],"While":[182],"clearly":[183],"$\\mathrm{cov}(G,H)":[184],"\\leqslant\\mathrm{cl}(G,H)$,":[185],"all":[186],"our":[188],"lower":[189],"apply":[193],"to":[194],"$\\mathrm{cov}(G,H)$":[195],"well.":[197]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}