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Article: Ramsey numbers involving large dense graphs and bipartite Turán numbers

TitleRamsey numbers involving large dense graphs and bipartite Turán numbers
Authors
Issue Date2003
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jctb
Citation
Journal Of Combinatorial Theory. Series B, 2003, v. 87 n. 2, p. 280-288 How to Cite?
AbstractWe prove that for any fixed integer m ≥ 3 and constants δ > 0 and α ≥ 0, if F is a graph on m vertices and G is a graph on n vertices that contains at least (δ - o(1))n2/(log n)α edges as n → ∞, then there exists a constant c = c(m, δ) > 0 such that r(F, G) ≥ (c - o(1)) (n/(log n)α+1)(e(F)-1)/(m-2) where e(F) is the number of edges F. We also show that for any fixed k ≥ m ≥ 2, r(Km,k,Kn) ≤ (k - 1 + o(1)) (n/log n)m as n → ∞. In addition, we establish the following result: For an m × k bipartite graph F with minimum degree s and for any E > 0, if k > m/E then ex(F;N) ≥ N2-1/s-e for all sufficiently large N. This partially proves a conjecture of Erdos and Simonovits. © 2002 Elsevier Science (USA). All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/156090
ISSN
2015 Impact Factor: 1.094
2015 SCImago Journal Rankings: 2.411
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorLi, Yen_US
dc.contributor.authorZang, Wen_US
dc.date.accessioned2012-08-08T08:40:22Z-
dc.date.available2012-08-08T08:40:22Z-
dc.date.issued2003en_US
dc.identifier.citationJournal Of Combinatorial Theory. Series B, 2003, v. 87 n. 2, p. 280-288en_US
dc.identifier.issn0095-8956en_US
dc.identifier.urihttp://hdl.handle.net/10722/156090-
dc.description.abstractWe prove that for any fixed integer m ≥ 3 and constants δ > 0 and α ≥ 0, if F is a graph on m vertices and G is a graph on n vertices that contains at least (δ - o(1))n2/(log n)α edges as n → ∞, then there exists a constant c = c(m, δ) > 0 such that r(F, G) ≥ (c - o(1)) (n/(log n)α+1)(e(F)-1)/(m-2) where e(F) is the number of edges F. We also show that for any fixed k ≥ m ≥ 2, r(Km,k,Kn) ≤ (k - 1 + o(1)) (n/log n)m as n → ∞. In addition, we establish the following result: For an m × k bipartite graph F with minimum degree s and for any E > 0, if k > m/E then ex(F;N) ≥ N2-1/s-e for all sufficiently large N. This partially proves a conjecture of Erdos and Simonovits. © 2002 Elsevier Science (USA). All rights reserved.en_US
dc.languageengen_US
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jctben_US
dc.relation.ispartofJournal of Combinatorial Theory. Series Ben_US
dc.titleRamsey numbers involving large dense graphs and bipartite Turán numbersen_US
dc.typeArticleen_US
dc.identifier.emailZang, W:wzang@maths.hku.hken_US
dc.identifier.authorityZang, W=rp00839en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1016/S0095-8956(02)00011-4en_US
dc.identifier.scopuseid_2-s2.0-0037374445en_US
dc.identifier.hkuros76703-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0037374445&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume87en_US
dc.identifier.issue2en_US
dc.identifier.spage280en_US
dc.identifier.epage288en_US
dc.identifier.isiWOS:000181209100007-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridLi, Y=7502087425en_US
dc.identifier.scopusauthoridZang, W=7005740804en_US

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