Bounding the Number of Minimal Transversals in Tripartite 3-Uniform Hypergraphs

完全三部图的三部图-圆交叉数的界

Bounding the tripartite-circle crossing number of complete tripartite graphs

本文研究了三部图在三个不相交圆上的三部图-圆绘制问题，给出了完全三部图$K_{m,n,p}$最小交叉数的上下界，并证明平衡受限3圆绘制并非最优。

Bounding the trace function of a hypergraph with applications

An upper bound on the trace function of a hypergraph $H$ is derived and its applications are demonstrated. For instance, a new upper bound for the VC dimension of $H$, or $vc(H)$, follows as a consequence and can be used to compute $vc(H)$ in polynomial time provided that $H$ has bounded degeneracy. This was not previously known. Particularly, when $H$ is a hypergraph arising from closed neighborhoods of a graph, this approach asymptotically improves the time complexity of the previous result for computing $vc(H)$. Another consequence is a general lower bound on the {\it distinguishing transve…