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Article: Ramsey numbers involving large dense graphs and bipartite Turán numbers
Title | Ramsey numbers involving large dense graphs and bipartite Turán numbers |
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Authors | |
Issue Date | 2003 |
Publisher | Academic 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? |
Abstract | We 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 Identifier | http://hdl.handle.net/10722/156090 |
ISSN | 2015 Impact Factor: 1.094 2015 SCImago Journal Rankings: 2.411 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
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dc.contributor.author | Li, Y | en_US |
dc.contributor.author | Zang, W | en_US |
dc.date.accessioned | 2012-08-08T08:40:22Z | - |
dc.date.available | 2012-08-08T08:40:22Z | - |
dc.date.issued | 2003 | en_US |
dc.identifier.citation | Journal Of Combinatorial Theory. Series B, 2003, v. 87 n. 2, p. 280-288 | en_US |
dc.identifier.issn | 0095-8956 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/156090 | - |
dc.description.abstract | We 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.language | eng | en_US |
dc.publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/jctb | en_US |
dc.relation.ispartof | Journal of Combinatorial Theory. Series B | en_US |
dc.title | Ramsey numbers involving large dense graphs and bipartite Turán numbers | en_US |
dc.type | Article | en_US |
dc.identifier.email | Zang, W:wzang@maths.hku.hk | en_US |
dc.identifier.authority | Zang, W=rp00839 | en_US |
dc.description.nature | link_to_subscribed_fulltext | en_US |
dc.identifier.doi | 10.1016/S0095-8956(02)00011-4 | en_US |
dc.identifier.scopus | eid_2-s2.0-0037374445 | en_US |
dc.identifier.hkuros | 76703 | - |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-0037374445&selection=ref&src=s&origin=recordpage | en_US |
dc.identifier.volume | 87 | en_US |
dc.identifier.issue | 2 | en_US |
dc.identifier.spage | 280 | en_US |
dc.identifier.epage | 288 | en_US |
dc.identifier.isi | WOS:000181209100007 | - |
dc.publisher.place | United States | en_US |
dc.identifier.scopusauthorid | Li, Y=7502087425 | en_US |
dc.identifier.scopusauthorid | Zang, W=7005740804 | en_US |