{"id":"https://openalex.org/W7204862330","doi":"https://doi.org/10.48550/arxiv.2608.29525","title":"Anti-Ramsey Number for Suspension of Edge-Critical Graphs","display_name":"Anti-Ramsey Number for Suspension of Edge-Critical Graphs","publication_year":2026,"publication_date":"2026-08-30","ids":{"openalex":"https://openalex.org/W7204862330","doi":"https://doi.org/10.48550/arxiv.2608.29525"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.29525","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29525","pdf_url":"https://arxiv.org/pdf/2608.29525","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.29525","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050604078","display_name":"Shuchao Li","orcid":"https://orcid.org/0000-0002-6856-0827","observed_orcids":["https://orcid.org/0000-0002-6856-0827"]},"institutions":[{"id":"https://openalex.org/I40963666","display_name":"Central China Normal University","ror":"https://ror.org/03x1jna21","country_code":"CN","type":"education","lineage":["https://openalex.org/I40963666"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li, Shuchao","raw_affiliation_strings":["School of Mathematics and Statistics, and Hubei Key Lab-Math. Sci. , Central China Normal University , Wuhan 430079 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, and Hubei Key Lab-Math. Sci. , Central China Normal University , Wuhan 430079 , China","institution_ids":["https://openalex.org/I40963666"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018763062","display_name":"Haojie Zheng","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I40963666","display_name":"Central China Normal University","ror":"https://ror.org/03x1jna21","country_code":"CN","type":"education","lineage":["https://openalex.org/I40963666"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zheng, Haojie","raw_affiliation_strings":["School of Mathematics and Statistics, and Hubei Key Lab-Math. Sci. , Central China Normal University , Wuhan 430079 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, and Hubei Key Lab-Math. Sci. , Central China Normal University , Wuhan 430079 , China","institution_ids":["https://openalex.org/I40963666"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I40963666"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9994999766349792,"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/T10374","display_name":"Advanced Graph Theory Research","score":9.999999747378752e-05,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":9.999999747378752e-05,"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/anti-ramsey-numbers","display_name":"anti-Ramsey numbers","score":0.9900000095367432},{"id":"https://openalex.org/keywords/rainbow-subgraphs","display_name":"rainbow subgraphs","score":0.6779999732971191},{"id":"https://openalex.org/keywords/edge-coloring","display_name":"edge coloring","score":0.5519999861717224},{"id":"https://openalex.org/keywords/edge-critical-graphs","display_name":"edge-critical graphs","score":0.9980000257492065},{"id":"https://openalex.org/keywords/turan-number","display_name":"Tur\u00e1n number","score":0.9470000267028809},{"id":"https://openalex.org/keywords/complete-graphs","display_name":"complete graphs","score":0.699999988079071},{"id":"https://openalex.org/keywords/friendship-graph","display_name":"friendship graph","score":0.8539999723434448},{"id":"https://openalex.org/keywords/chromatic-number","display_name":"chromatic number","score":0.6000000238418579}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8235999941825867},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7405999898910522},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5134000182151794},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5090000033378601},{"id":"https://openalex.org/C2779623528","wikidata":"https://www.wikidata.org/wiki/Q864377","display_name":"Multiset","level":2,"score":0.48489999771118164},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.4708999991416931},{"id":"https://openalex.org/C168291704","wikidata":"https://www.wikidata.org/wiki/Q902252","display_name":"Complement graph","level":5,"score":0.42309999465942383},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4115999937057495},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.40380001068115234},{"id":"https://openalex.org/C148364342","wikidata":"https://www.wikidata.org/wiki/Q948887","display_name":"Wheel graph","level":5,"score":0.37229999899864197},{"id":"https://openalex.org/C125080357","wikidata":"https://www.wikidata.org/wiki/Q45715","display_name":"Complete graph","level":3,"score":0.3628000020980835},{"id":"https://openalex.org/C14201764","wikidata":"https://www.wikidata.org/wiki/Q1205074","display_name":"Symmetric graph","level":5,"score":0.34599998593330383},{"id":"https://openalex.org/C128067373","wikidata":"https://www.wikidata.org/wiki/Q1415372","display_name":"Path graph","level":5,"score":0.3292999863624573},{"id":"https://openalex.org/C123482549","wikidata":"https://www.wikidata.org/wiki/Q826467","display_name":"Regular graph","level":5,"score":0.3255999982357025},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.3246999979019165},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.3203999996185303},{"id":"https://openalex.org/C121134508","wikidata":"https://www.wikidata.org/wiki/Q4949882","display_name":"Bound graph","level":5,"score":0.3149999976158142},{"id":"https://openalex.org/C161677786","wikidata":"https://www.wikidata.org/wiki/Q2478475","display_name":"Neighbourhood (mathematics)","level":2,"score":0.3140999972820282},{"id":"https://openalex.org/C18819970","wikidata":"https://www.wikidata.org/wiki/Q3035340","display_name":"Butterfly graph","level":5,"score":0.313400000333786},{"id":"https://openalex.org/C80763892","wikidata":"https://www.wikidata.org/wiki/Q958394","display_name":"Hypercube graph","level":5,"score":0.30570000410079956},{"id":"https://openalex.org/C56783289","wikidata":"https://www.wikidata.org/wiki/Q3115556","display_name":"Distance-regular graph","level":5,"score":0.3027999997138977},{"id":"https://openalex.org/C103257674","wikidata":"https://www.wikidata.org/wiki/Q6934937","display_name":"Multiple edges","level":3,"score":0.2989000082015991},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.2919999957084656},{"id":"https://openalex.org/C100500283","wikidata":"https://www.wikidata.org/wiki/Q1374495","display_name":"Cubic graph","level":5,"score":0.2912999987602234},{"id":"https://openalex.org/C140752511","wikidata":"https://www.wikidata.org/wiki/Q905837","display_name":"Graph minor","level":5,"score":0.2782999873161316},{"id":"https://openalex.org/C17169500","wikidata":"https://www.wikidata.org/wiki/Q3033506","display_name":"Null graph","level":5,"score":0.2761000096797943},{"id":"https://openalex.org/C2777724877","wikidata":"https://www.wikidata.org/wiki/Q2548661","display_name":"Crossing number (knot theory)","level":3,"score":0.26969999074935913},{"id":"https://openalex.org/C19332903","wikidata":"https://www.wikidata.org/wiki/Q7623247","display_name":"Strength of a graph","level":5,"score":0.2630999982357025},{"id":"https://openalex.org/C73380178","wikidata":"https://www.wikidata.org/wiki/Q8024306","display_name":"Windmill graph","level":5,"score":0.2578999996185303}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.29525","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29525","pdf_url":"https://arxiv.org/pdf/2608.29525","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.29525","doi":"https://doi.org/10.48550/arxiv.2608.29525","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.29525","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.29525","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29525","pdf_url":"https://arxiv.org/pdf/2608.29525","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3399293828","display_name":null,"funder_award_id":"12171190","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3552376439","display_name":null,"funder_award_id":"12571365","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204862330.pdf","grobid_xml":"https://content.openalex.org/works/W7204862330.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4404407605","https://openalex.org/W4415310396"],"related_works":["https://openalex.org/W4404407605","https://openalex.org/W4404443690","https://openalex.org/W1526995523","https://openalex.org/W4404822223","https://openalex.org/W7214794479","https://openalex.org/W1595352724","https://openalex.org/W2365696220","https://openalex.org/W3103475865","https://openalex.org/W2038229259","https://openalex.org/W4415310396"],"abstract_inverted_index":{"An":[0],"edge-colored":[1],"graph":[2,7,24,44,61,74,102],"is":[3,31,65,100],"called":[4],"a":[5,22,27,81,84,88,171,183],"rainbow":[6,49],"if":[8],"all":[9,110],"its":[10],"edges":[11,70],"have":[12],"distinct":[13],"colors.":[14],"The":[15],"\\textit{anti-Ramsey":[16],"number},":[17,56],"denoted":[18,57],"by":[19,58,104],"$\\ar(n,F),$":[20],"for":[21,60,114,147,157],"fixed":[23],"$F$":[25,62,79],"and":[26,63,87,123,128,145,162,169,182],"positive":[28],"integer":[29],"$n$,":[30,64],"the":[32,42,54,66,93,101,106,179,191],"maximum":[33,67],"number":[34,68],"of":[35,41,51,69,91,98,112,173,185],"colors":[36],"used":[37],"in":[38,71],"an":[39,72],"edge-coloring":[40],"complete":[43],"$K_n$":[45],"that":[46,75,130],"contains":[47],"no":[48],"copy":[50],"$F$.":[52],"Meanwhile,":[53],"\\textit{Tur\u00e1n":[55],"$\\ex(n,F),$":[59],"$n$-vertex":[73],"does":[76],"not":[77],"contain":[78],"as":[80],"subgraph.":[82],"For":[83],"vertex":[85,107],"$v$":[86,108],"multiset":[89],"$\\mathcal{H}$":[90,99],"graphs,":[92,144],"\\textit{suspension}":[94],"$\\mathcal{H}":[95],"+":[96],"v$":[97],"obtained":[103],"connecting":[105],"to":[109],"vertices":[111],"$H$":[113],"each":[115],"$H":[116],"\\in":[117],"\\mathcal{H}$.":[118],"Let":[119],"integers":[120],"$k\\ge":[121,158],"1$":[122],"$r\\ge":[124,160],"2$":[125,161],"be":[126],"fixed,":[127],"suppose":[129],"$\\mathcal{H}_{k+1}=\\{H_1,":[131],"H_2,":[132,137],"\\ldots,":[133,138],"H_{k+1}\\}+v$":[134],"satisfying":[135],"$H_1,":[136],"H_{k+1}$":[139],"are":[140],"pairwise":[141],"vertex-disjoint":[142],"edge-critical":[143],"$\u03c7(H_i)=r$":[146],"$i=1,2,\\ldots,":[148],"k+1$.In":[149],"this":[150],"paper,":[151],"we":[152],"determine":[153],"$":[154,156],"\\ar(n,\\mathcal{H}_{k+1})":[155],"1$,":[159],"sufficiently":[163],"large":[164],"$n$.":[165],"This":[166],"result":[167,172,184],"unifies":[168],"generalizes":[170],"Liu":[174],"et":[175,187],"al.":[176,188],"(arXiv:2411.08475)":[177],"concerning":[178],"friendship":[180],"graph,":[181],"Lu":[186],"(arXiv:2507.13165)":[189],"on":[190],"intersecting":[192],"cliques.":[193]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}
