数学研究
數學研究
수학연구
JOURNAL OF MATHEMATICAL STUDY
2010年
2期
114-121
,共8页
彩色的%一致超图%哈密顿圈
綵色的%一緻超圖%哈密頓圈
채색적%일치초도%합밀돈권
Multicolored%uniform hypergraphs%Hamilton cycles
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.
假設c是一箇小于1/1152的常數.證明:對于每箇充分大的偶數n,如果一箇具有n箇頂點的3一緻完全超圖的邊著色滿足每種顏色齣現的次數不超過[cn],那麽必含有一箇每條邊顏色都不一樣的綵色哈密頓圈.
가설c시일개소우1/1152적상수.증명:대우매개충분대적우수n,여과일개구유n개정점적3일치완전초도적변착색만족매충안색출현적차수불초과[cn],나요필함유일개매조변안색도불일양적채색합밀돈권.
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.
