Xiong and Liu[21]gave a characterization of the graphs G for which the n-iterated line graph L^(n)(G)is hamiltonian,for n≥2.In this paper,we study the existence of a hamiltonian path in L^(n)(G),and give a characteri...Xiong and Liu[21]gave a characterization of the graphs G for which the n-iterated line graph L^(n)(G)is hamiltonian,for n≥2.In this paper,we study the existence of a hamiltonian path in L^(n)(G),and give a characterization of G for which L^(n)(G)has a hamiltonian path.As applications,we use this characterization to give several upper bounds on the hamiltonian path index of a graph.展开更多
The Maslov P-index theory for a symplectic path is defined. Various properties of this index theory such as homotopy invariant, symplectic additivity and the relations with other Morse indices are studied. As an appli...The Maslov P-index theory for a symplectic path is defined. Various properties of this index theory such as homotopy invariant, symplectic additivity and the relations with other Morse indices are studied. As an application, the non-periodic problem for some asymptotically linear Hamiltonian systems is considered.展开更多
A graph G is {K1,4, K1,4 ＋ e}-free if G contains no induced subgraph isomorphic to K1,4 or KI,a ＋ e In this paper, we show that G has a path which is either hamiltonian or of length at least 25（G） ＋ 2 if G is a c...A graph G is {K1,4, K1,4 ＋ e}-free if G contains no induced subgraph isomorphic to K1,4 or KI,a ＋ e In this paper, we show that G has a path which is either hamiltonian or of length at least 25（G） ＋ 2 if G is a connected {K1,4, K1,4 ＋ e}-free graph on at least 7 vertices.展开更多
提出基于笔段结构的手写体数字字符笔迹信息重构方法.首先采用改进的特征点提取算法,准确快速地从骨骼图像提取完整的特征点集合,从而保证了可靠的字符笔段结构恢复,并根据笔段结构图构建笔段关系图.在本文基于笔段的笔迹重构方法中,笔...提出基于笔段结构的手写体数字字符笔迹信息重构方法.首先采用改进的特征点提取算法,准确快速地从骨骼图像提取完整的特征点集合,从而保证了可靠的字符笔段结构恢复,并根据笔段结构图构建笔段关系图.在本文基于笔段的笔迹重构方法中,笔迹重构实质上就是笔段的排序问题.将笔迹重构视为一个全局最优问题,采用总体方向变化最小路径重构书写笔迹.该问题通过搜寻最小代价 Hamilton 路径来解决,等同于解所构建图中的旅行售货郎问题.在 UCI 测试集上的实验表明,本文方法对于手写体数字字符的笔迹重构是有效的.展开更多
For a graph G, we denote by p（G） and c（G） the number of vertices of a longest path and a longest cycle in G, respectively. For a vertex v in G, id（v） denotes the implicit degree of v. In this paper, we obtain th...For a graph G, we denote by p（G） and c（G） the number of vertices of a longest path and a longest cycle in G, respectively. For a vertex v in G, id（v） denotes the implicit degree of v. In this paper, we obtain that if G is a 2-connected graph on n vertices such that the implicit degree sum of any three independent vertices is at least n ＋ 1, then either G contains a hamiltonian path, or c（G） 〉 p（G） - 1.展开更多
基金Supported by the Natural Science Foundation of China(12131013,12371356)the special fund for Science and Technology Innovation Teams of Shanxi Province(202204051002015)the Fundamental Research Program of Shanxi Province(202303021221064).
文摘Xiong and Liu[21]gave a characterization of the graphs G for which the n-iterated line graph L^(n)(G)is hamiltonian,for n≥2.In this paper,we study the existence of a hamiltonian path in L^(n)(G),and give a characterization of G for which L^(n)(G)has a hamiltonian path.As applications,we use this characterization to give several upper bounds on the hamiltonian path index of a graph.
基金Project supported by the National Natural Science Foundation of China (No.10531050) and FANEDD.
文摘The Maslov P-index theory for a symplectic path is defined. Various properties of this index theory such as homotopy invariant, symplectic additivity and the relations with other Morse indices are studied. As an application, the non-periodic problem for some asymptotically linear Hamiltonian systems is considered.
基金Supported by Scientific Research Program of the Higher Education Institution of Xinjiang (Grant No. 2011S30)Science Foundation of Xinjiang Normal University
文摘A graph G is {K1,4, K1,4 ＋ e}-free if G contains no induced subgraph isomorphic to K1,4 or KI,a ＋ e In this paper, we show that G has a path which is either hamiltonian or of length at least 25（G） ＋ 2 if G is a connected {K1,4, K1,4 ＋ e}-free graph on at least 7 vertices.
基金Supported by the National Natural Science Foundation of China(11071002)the NFS of Anhui Province(11040606M14)+4 种基金the NSF of Department of Education of Anhui Province(KJ2011A195)the Program for New Century Excellent Talents in University(NCET-10-0001)the Key Project of Chinese Ministry of Education(210091)the Specialized Research Fund for the Doctoral Program of Higher Education(20103401110002)the Scientific Research Fund for Fostering Distinguished Young Scholars of Anhui University(KJJQ1001)
文摘提出基于笔段结构的手写体数字字符笔迹信息重构方法.首先采用改进的特征点提取算法,准确快速地从骨骼图像提取完整的特征点集合,从而保证了可靠的字符笔段结构恢复,并根据笔段结构图构建笔段关系图.在本文基于笔段的笔迹重构方法中,笔迹重构实质上就是笔段的排序问题.将笔迹重构视为一个全局最优问题,采用总体方向变化最小路径重构书写笔迹.该问题通过搜寻最小代价 Hamilton 路径来解决,等同于解所构建图中的旅行售货郎问题.在 UCI 测试集上的实验表明,本文方法对于手写体数字字符的笔迹重构是有效的.
基金supported by the National Natural Science Foundation of China(Grant No.11501322)the Postdoctoral Science Foundation of China(Grant No.2015M571999)the Natural Science Foundation of Shandong Province(Grant No.ZR2014AP002)
文摘For a graph G, we denote by p（G） and c（G） the number of vertices of a longest path and a longest cycle in G, respectively. For a vertex v in G, id（v） denotes the implicit degree of v. In this paper, we obtain that if G is a 2-connected graph on n vertices such that the implicit degree sum of any three independent vertices is at least n ＋ 1, then either G contains a hamiltonian path, or c（G） 〉 p（G） - 1.
