Abstract
The Turán number for a graph H, denoted by \(\text {ex}(n,H)\), is the maximum number of edges in any simple graph with n vertices which doesn’t contain H as a subgraph. In this paper we find the lower and upper bounds for \(\text { ex}(n,W_{2t+1})\). We show that if \(n\ge 4t\), then \(\text { ex}(n,W_{2t+1})\ge \left\lfloor \lfloor \frac{2n+t}{4}\rfloor (n+\frac{t-1}{2}-\lfloor \frac{2n+t}{4}\rfloor )\right\rfloor +1.\) We also show that for sufficiently large n and \(t\ge 5\), \(\text { ex}(n,W_{2t+1})\le \frac{ n^2 }{4}+{t-1\over 2}n\). Moreover we find the exact value of the Turán number for \(W_9\). That is, we show that for sufficiently large n, \(\text { ex}(n,W_9)= \lfloor \frac{n^2}{4}\rfloor +\lceil \frac{3}{4}n\rceil +1\).
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This work was supported by Korea University Grant.
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Kim, B.M., Song, B.C. & Hwang, W. The Lower and Upper Bounds of Turán Number for Odd Wheels. Graphs and Combinatorics 37, 919–932 (2021). https://doi.org/10.1007/s00373-021-02290-0
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DOI: https://doi.org/10.1007/s00373-021-02290-0