3一致完全超图的彩色哈密顿圈(英文)

Multicolored Hamilton cycles of the Complete 3-uniform Hypergraph

假设c是一个小于1/1152的常数.证明:对于每个充分大的偶数n,如果一个具有n个顶点的3一致完全超图的边着色满足每种颜色出现的次数不超过[cn],那么必含有一个每条边颜色都不一样的彩色哈密顿圈.

The hyperedges of the complete 3-uniform hypergraph are colored so that no color appears more than [cn] times, where c 〈 1/1152 is a constant. We show that ifn is a sufficiently large even number, then there is a hamiltonian cycle in which each edge is of a different color.