设A和B是两个集合, A和B的对称差是由$A\cup B$中所有不属于$A\cap B$的元素组成的一个集合, 记为$A\Delta B$。若一个超图不含有三条互不相同的边A, B, C使得$A\Delta B\subset C$, 则称该超图是一个可消去超图。一个3-一致可消去超图同时不含$F_4=\{abc, abd, bcd\}$和$F_5=\{abc, abd, cde\}$作为子超图。Bollobás (1974) 给出了3-一致可消去超图的最大边数, 并得出平衡的完全3-部3-一致超图是唯一达到最大边数的3-一致可消去超图。Keevash和Mubayi (2004) 进一步确定了平衡的完全3-部3-一致超图是唯一不含$F_5$作为子超图且边数达到最大的3-一致超图。设$\mathcal{H}$是一个超图, W是顶点集$V(\mathcal{H})$的一个非空子集。如果超图$\mathcal{H}$中的任意一条边只包含W中的一个顶点, 则称W是超图$\mathcal{H}$的一个独立横贯。在本文中, 我们得到了具有独立横贯的3-一致可消去超图p-谱半径的最大值。进一步, 我们证明了当p>2时, 平衡的完全3-部3-一致超图是唯一具有独立横贯且p-谱半径达到最大的3-一致可消去超图。

Let A and B be two sets, the symmetry difference of A and B is a set consisting of all elements not belonging to $A\cap B$ in $A\cup B$, denoted by $A\Delta B$. A hypergraph is called a cancellative hypergraph, if it contains no three distinct edges A, B, and C, such that $A\Delta B\subset C$. In fact, a cancellative3-uniform hypergraph contains neither $F_4=\{abc, abd, bcd\}$ nor $F_5=\{abc, abd, cde\}$ as its subgraphs. Bollobás (1974) determined the maximum number of edges in a cancellative3-uniform hypergraph, and got that only the balanced complete3-partite3-uniform hypergraph achieved the maximum number of edges in a cancellative3-uniform hypergraph. Furthermore, Keevash and Mubayi (2004) determined that only the balanced complete3-partite3-uniform hypergraph achieved the maximum number of edges in a3-uniform hypergraph containing no copy of $F_5$. Let $\mathcal{H}$ be a hypergraph, and W be a nonempty subset of $V(\mathcal{H})$. If every edge in $\mathcal{H}$ contains exactly one vertex in W, then we call W an independent transversal of $\mathcal{H}$. In this paper, we determine the maximump-spectral radius of a cancellative3-uniform hypergraph with an independent transversal. Furthermore, if $p>2$, we get that only the balanced complete3-partite3-uniform hypergraph achieved the maximump-spectral radius of a cancellative3-uniform hypergraph with an independent transversal.