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A bound on the number of edges in graphs without an even cycle
- Source :
- Combin. Probab. Comput. 26 (2017), no. 1, 1-15
- Publication Year :
- 2014
-
Abstract
- We show that, for each fixed $k$, an $n$-vertex graph not containing a cycle of length $2k$ has at most $80\sqrt{k}\log k\cdot n^{1+1/k}+O(n)$ edges.<br />Comment: 16 pages, v2 appeared in Comb. Probab. Comp., v3 fixes an error in v2 and explains why the method in the paper cannot improve the power of k further, v4 fixes the proof of Theorem 12 introduced in v3
- Subjects :
- Mathematics - Combinatorics
05C35, 05D99, 05C38
Subjects
Details
- Database :
- arXiv
- Journal :
- Combin. Probab. Comput. 26 (2017), no. 1, 1-15
- Publication Type :
- Report
- Accession number :
- edsarx.1403.1601
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1017/S0963548316000134