The Lower and Upper Bounds of Turan Number for Odd Wheels

Abstract

The Turan number for a graph H, denoted by 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 ex(n, W-2t(+1)). We show that if n >= 4t, then ex(n, W-2t(+1)) >= left perpendicular left perpendicular2n+t/4right perpendicular (n + t-1/2 - left perpendicular2n+t/4right perpendicular)right perpendicular + 1. We also show that for sufficiently large n and t >= 5, ex(n, W-2t(+1)) <= n(2)/4 + t-1/2n. Moreover we find the exact value of the Turan number for W-9. That is, we show that for sufficiently large n, ex(n, W-9) = left perpendicularn(2)/4right perpendicular [3/4n] + 1.