Let $G=\left(V,E\right)$ be a $\tau$‐critical graph with $\tau \left(G\right)=t$. Erdős and Gallai proved that $\mid V\mid \le 2t$ and the bound $\mid E\mid \le \left(\genfrac{}{}{0ex}{}{t+1}{2}\right)$ was obtained by Erdős, Hajnal, and Moon. We give here the sharp combined bound $\mid E\mid +\mid V\mid \le \left(\genfrac{}{}{0ex}{}{t+2}{2}\right)$ and find all graphs with equality.

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阶图加上τ临界图的大小

让 $G=（V，Ë）$ 成为 $\tau$关键图 $\tau （G）=Ť$。Erdős和Gallai证明了$\mid V\mid \le 2Ť$ 和界限 $\mid Ë\mid \le \left(\genfrac{}{}{0ex}{}{Ť+\mathrm{1个}}{2}\right)$由Erdős，Hajnal和Moon获得。我们在这里给出了清晰的组合边界$\mid Ë\mid +\mid V\mid \le \left(\genfrac{}{}{0ex}{}{Ť+2}{2}\right)$ 并找到所有相等的图