Hamiltonian cycles in the generating graphs of finite groups
نویسندگان
چکیده
منابع مشابه
Generating Hamiltonian Cycles in Complete Graphs
We prove that hamiltonian cycles of complete graphs can be generated in a Gray code manner by means of small local interchanges.
متن کاملSome combinatorial aspects of finite Hamiltonian groups
In this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite Hamiltonian group. The coverings with three proper subgroups and the principal series of such a group are also counted. Finally, we give a complete description of the lattice of characteristic subgroups of a finite H...
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 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: Bulletin of the London Mathematical Society
سال: 2010
ISSN: 0024-6093
DOI: 10.1112/blms/bdq017