منابع مشابه
Hamiltonian Cycles in T-Graphs
There is only one finite, 2-connected, linearly convex graph in the Archimedean triangular tiling that does not have a Hamiltonian cycle. The vertices and polygonal edges of the planar Archimedean tilings 44 and 36 of the plane, partially shown in Figs. 1 and 2, respectively, are called the square tiling graph (STG) and the triangular tiling graph (TTG). (See [1].) A subgraph G of TTG is linear...
متن کاملLong Cycles in Hamiltonian Graphs
We prove that if an n-vertex graph with minimum degree at least 3 contains a Hamiltonian cycle, then it contains another cycle of length n− o(n); in particular, this verifies, in an asymptotic form, a well-known conjecture due to Sheehan from 1975.
متن کاملSmall Cycles in Hamiltonian Graphs
We prove that if a graph G on n > 32 vertices is hamiltonian and has two nonadjacent vertices u and u with d(u) + d(u) 3 n + z where z = 0 if n is odd and z = 1 if n is even, then G contains all cycles of length m where 3 < m < 1/5(n + 13).
متن کاملHamiltonian Cycles in Sparse Graphs
Hamiltonian Cycles in Sparse Graphs Alexander Hertel Master of Science Graduate Department of Computer Science University of Toronto 2004 The subject of this thesis is the Hamiltonian Cycle problem, which is of interest in many areas including graph theory, algorithm design, and computational complexity. Named after the famous Irish mathematician Sir William Rowan Hamilton, a Hamiltonian Cycle ...
متن کاملDisjoint Hamiltonian cycles in graphs
Let G be a 2(k + I)-connected graph of order n. It is proved that if uv rJ. E(G) implies that max{d(u), d(v)} ?: ~ + 2k then G contains k + 1 pairwise disjoint Hamiltonian cycles when c5 (G) ?: 4k + 3. 1 .. Introduction All graphs we consider are finite and simple. We use standard terminology and notation from Bondy and Murty [2] except as indicated. Let G = (V(G), E(G)) be a graph with vertex ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2000
ISSN: 0179-5376
DOI: 10.1007/s004540010051