Let \(r(K_{p,q},t)\) be the maximum number of colors in an edge-coloring of the complete bipartite graph \(K_{p,q}\) not having t edge-disjoint rainbow spanning trees. We prove that \(r(K_{p,p},1)=p^2-2p+2\) for \(p\ge 4\) and \(r(K_{p,q},1)=pq-2q+1\) for \(p>q\ge 4\). Let \(t\ge 2\). We also show that \(r(K_{p,p},t)=p^2-2p+t+1\) for \(p \ge 2t+\sqrt{3t-3}+4\) and \(r(K_{p,q},t)=pq-2q+t\) for \(p > q \ge 2t+\sqrt{3t-2}+4\).

中文翻译：

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t边缘不相交的彩虹生成树的完全二部图中的反Ramsey问题

令\（r（K_ {p，q}，t）\）是完整二部图\（K_ {p，q} \）的边着色中没有t边不相交彩虹跨越的最大颜色数树木。我们证明了\（R（K_ {P，P}，1）= P ^ 2-2p + 2 \）为\（P \ GE 4 \）和\（R（K_ {P，Q}，1）= pq-2q + 1 \）表示\（p> q \ ge 4 \）。让\（t \ ge 2 \）。我们还证明\（r \（k_ {p，p}，t）= p ^ 2-2p + t + 1 \）对于\（p \ ge 2t + \ sqrt {3t-3} +4 \）和\（ R（K_ {p，q}，T）= PQ-2Q + T \）为\（p> q \ GE 2T + \ SQRT {3T-2} 4 \）。