共查询到20条相似文献,搜索用时 31 毫秒
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Thomassen proved that a strong tournament has a pair of arc-disjoint Hamiltonian paths with distinct initial vertices and distinct terminal vertices if and only if is not an almost transitive tournament of odd order, where an almost transitive tournament is obtained from a transitive tournament with acyclic ordering (i.e., for all ) by reversing the arc . A digraph is a local tournament if for every vertex of , both the out-neighbors and the in-neighbors of induce tournaments. Bang-Jensen, Guo, Gutin and Volkmann split local tournaments into three subclasses: the round decomposable; the non-round decomposable which are not tournaments; the non-round decomposable which are tournaments. In 2015, we proved that every 2-strong round decomposable local tournament has a Hamiltonian path and a Hamiltonian cycle which are arc-disjoint if and only if it is not the second power of an even cycle. In this paper, we discuss the arc-disjoint Hamiltonian paths in non-round decomposable local tournaments, and prove that every 2-strong non-round decomposable local tournament contains a pair of arc-disjoint Hamiltonian paths with distinct initial vertices and distinct terminal vertices. This result combining with the one on round decomposable local tournaments extends the above-mentioned result of Thomassen to 2-strong local tournaments. 相似文献
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Vizing conjectured that every edge chromatic critical graph contains a 2-factor. Believing that stronger properties hold for this class of graphs, Luo and Zhao (2013) showed that every edge chromatic critical graph of order with maximum degree at least is Hamiltonian. Furthermore, Luo et al. (2016) proved that every edge chromatic critical graph of order with maximum degree at least is Hamiltonian. In this paper, we prove that every edge chromatic critical graph of order with maximum degree at least is Hamiltonian. Our approach is inspired by the recent development of Kierstead path and Tashkinov tree techniques for multigraphs. 相似文献
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Given a graph , let be the set of all cycle lengths contained in and let . Let and let be the greatest common divisor of and all the positive pairwise differences of elements in . We prove that if a Hamiltonian graph of order has at least edges, where is an integer such that , then or is exceptional, by which we mean for some . We also discuss cases where is not exceptional, for example when is prime. Moreover, we show that , which if is bipartite implies that , where is the number of edges in . 相似文献
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In this paper we are concerned with the periodic Hamiltonian system with one degree of freedom, where the origin is a trivial solution. We assume that the corresponding linearized system at the origin is elliptic, and the characteristic exponents of the linearized system are with ω be a Diophantine number, moreover if the system is formally linearizable, then it is analytically linearizable. As a result, the origin is always stable in the sense of Liapunov in this case. 相似文献
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For a subgraph of , let be the maximum number of vertices of that are pairwise distance at least three in . In this paper, we prove three theorems. Let be a positive integer, and let be a subgraph of an -connected claw-free graph . We prove that if , then either can be covered by a cycle in , or there exists a cycle in such that . This result generalizes the result of Broersma and Lu that has a cycle covering all the vertices of if . We also prove that if , then either can be covered by a path in , or there exists a path in such that . By using the second result, we prove the third result. For a tree , a vertex of with degree one is called a leaf of . For an integer , a tree which has at most leaves is called a -ended tree. We prove that if , then has a -ended tree covering all the vertices of . This result gives a positive answer to the conjecture proposed by Kano et al. (2012). 相似文献
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We study the dynamics of a class of Hamiltonian systems with dissipation, coupled to noise, in a singular (small mass) limit. We derive the homogenized equation for the position degrees of freedom in the limit, including the presence of a noise-induced drift term. We prove convergence to the solution of the homogenized equation in probability and, under stronger assumptions, in an -norm. Applications cover the overdamped limit of particle motion in a time-dependent electromagnetic field, on a manifold with time-dependent metric, and the dynamics of nuclear matter. 相似文献
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A forced cycle of a graph is a cycle in such that has a unique perfect matching. A graph is a cycle-forced graph if every cycle in is a forced cycle. In this paper, we give a characterization of cycle-forced hamiltonian bipartite graphs. 相似文献
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We call a graph pancyclic if it contains at least one cycle of every possible length , for . In this paper, we define a new property called chorded pancyclicity. We explore forbidden subgraphs in claw-free graphs sufficient to imply that the graph contains at least one chorded cycle of every possible length . In particular, certain paths and triangles with pendant paths are forbidden. 相似文献