关于图是可迹或1-哈密尔顿的两个充分条件(英文)

设 G是一个图 ,G的独立集 Y称为本质集 ,如果存在 { y1 ,y2 } Y,使得 dist( y1 ,y2 ) =2 .利用插点方法 ,给出了关于 ( k-1 )或 ( k+ 1 ) -连通 ( k≥ 2 )图 G是可迹的或 1 -哈密尔顿的统一证明 .

The Integrable in Liouville Sense of a Finite-dimensional Hamilton System

Based on a 2 × 2 eigenvalue problem,a set of（1 ＋ 1）-dimensional soliton equations are proposed.Moreover,we obtain a finite dimensional Hamilton system with the help of nonlinearization approach.Then the generating function approach and the way to straighten out of Fm-flow are used to prove the involutivity and the functional independence of conserved integrals for the finite-dimensional Hamilton system,hence,we can verify it is completely integrable in Liouville sense.