Volume 4 Number 3 (May 2014)
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IJAPM 2014 Vol.4(3): 211-214 ISSN: 2010-362X
DOI: 10.7763/IJAPM.2014.V4.285

On the Turán Numbers for Even Cycles

Rui Zhang, Yongqi Sun, and Yali Wu
Abstract—For integers k≥2 and n≥2k+1, let ex (n, C2k) denote the maximum number of edges in a C2k-free graph of order n, and EX (n, C2k) denote the set of all graphs with ex (n, C2k) edges. For k=3, it is well known that ex (n, C2k) > 0.5338n1+1/k for some large n. In this paper, we study the values of ex (n, C2k) for k≥3 when n is small, their lower bounds were given based the three graphs without C2k. The known result shows that it is the tight lower bound for k=3 and n=28, and we further conjecture that ex (n, C2k)=(2k+1)(2k−1)(2k−2)/2 for n=4k2−2k−2 and k≥4.

Index Terms—Extremal graph, even cycle, lower bounds, Turán numbers.

The authors are with Beijing Jiaotong University, China (e-mail: yqsun@bjtu.edu.cn).

Cite: Rui Zhang, Yongqi Sun, and Yali Wu, "On the Turán Numbers for Even Cycles," International Journal of Applied Physics and Mathematics vol. 4, no. 3, pp. 211-214, 2014.

General Information

ISSN: 2010-362X (Online)
Abbreviated Title: Int. J. Appl. Phys. Math.
Frequency: Quarterly
DOI: 10.17706/IJAPM
Editor-in-Chief: Prof. Haydar Akca 
Abstracting/ Indexing:  Index Copernicus, EI (INSPEC, IET), Chemical Abstracts Services (CAS), Nanowerk Database, Google Scholar, EBSCO, etc.
E-mail: ijapm@iap.org
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