TY - JOUR
T1 - Extremal results for odd cycles in sparse pseudorandom graphs
AU - Aigner-Horev, Elad
AU - Hàn, Hiêp
AU - Schacht, Mathias
N1 - Funding Information:
1 Supported by FAPESP (Proc. 2010/16526-3) and by NUMEC/USP, lagem Estocástica e Complexidade of the University of São Paulo. 2Email: elad.horev|[email protected] 3Email: [email protected]
PY - 2013/11/5
Y1 - 2013/11/5
N2 - We consider extremal problems for subgraphs of pseudorandom graphs. Our results implies that for (n, d, λ)-graphs Γ satisfying. λ2k-1≪d2kn(logn)-2(k-1)(2k-1) any subgraph G⊂. Γ not containing a cycle of length 2. k+. 1 has relative density at most 12+o(1). Up to the polylog-factor the condition on λ is best possible and was conjectured by Krivelevich, Lee and Sudakov.
AB - We consider extremal problems for subgraphs of pseudorandom graphs. Our results implies that for (n, d, λ)-graphs Γ satisfying. λ2k-1≪d2kn(logn)-2(k-1)(2k-1) any subgraph G⊂. Γ not containing a cycle of length 2. k+. 1 has relative density at most 12+o(1). Up to the polylog-factor the condition on λ is best possible and was conjectured by Krivelevich, Lee and Sudakov.
KW - Extremal graph theory
KW - Odd cycles
KW - Pseudorandom graphs
UR - https://www.scopus.com/pages/publications/84887167768
U2 - 10.1016/j.endm.2013.10.060
DO - 10.1016/j.endm.2013.10.060
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AN - SCOPUS:84887167768
SN - 1571-0653
VL - 44
SP - 385
EP - 391
JO - Electronic Notes in Discrete Mathematics
JF - Electronic Notes in Discrete Mathematics
ER -