The theta graph ${\Theta _{\ell ,t}}$ consists of two vertices joined by t vertex-disjoint paths, each of length $\ell $ . For fixed odd $\ell $ and large t, we show that the largest graph not containing ${\Theta _{\ell ,t}}$ has at most ${c_\ell }{t^{1 - 1/\ell }}{n^{1 + 1/\ell }}$ edges and that this is tight apart from the value of ${c_\ell }$ .

中文翻译：

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图兰数的 theta 图

θ图${\Theta _{\ell ,t}}$由两个连接的顶点组成吨顶点不相交的路径，每个长度$\ell $. 对于固定奇数$\ell $和大吨，我们证明最大的图不包含${\Theta _{\ell ,t}}$最多有${c_\ell }{t^{1 - 1/\ell }}{n^{1 + 1/\ell }}$边缘，这是紧除了的价值${c_\ell }$.