Automorphism groups with cyclic commutator subgroup and Hamilton cycles

自同构群以 $\boldsymbol{\text{Z}_{p}}$ 为换位子群的传递图的哈密顿性

Hamiltonicity of Transitive Graphs Whose Automorphism Group Has $\Z_{p}$ as Commutator Subgroups

本研究将Durnberger关于素数阶换位子群有限群的连通Cayley图含哈密顿圈的结论，推广到无限情形及自同构群含素数阶循环换位子群传递子群的更广泛无限图类。

Cayley graphs on nilpotent groups with cyclic commutator subgroup are hamiltonian

We show that if G is any nilpotent, finite group, and the commutator subgroup of G is cyclic, then every connected Cayley graph on G has a hamiltonian cycle.

Cayley graphs on groups with commutator subgroup of order 2p are hamiltonian

We show that if G is a finite group whose commutator subgroup [G,G] has order 2p, where p is an odd prime, then every connected Cayley graph on G has a hamiltonian cycle.

Odd-order Cayley graphs with commutator subgroup of order pq are hamiltonian

We show that if G is a nontrivial, finite group of odd order, whose commutator subgroup [G,G] is cyclic of order p^m q^n, where p and q are prime, then every connected Cayley graph on G has a hamiltonian cycle.

On the full automorphism group of a Hamiltonian cycle system of odd order

It is shown that a necessary condition for an abstract group G to be the full automorphism group of a Hamiltonian cycle system is that G has odd order or it is either binary, or the affine linear group AGL(1; p) with p prime. We show that this condition is also sufficient except possibly for the class of non-solvable binary groups.

计算三次图的哈密顿压缩因子

Computing the Hamiltonian compression factors of cubic graphs

提出一种计算在自同构作用下作为旋转不变的哈密顿圈的算法，并用于计算图的哈密顿压缩因子。以所有三次边传递图为例，计算了除两个非哈密顿图和98个仅给出下界的图外的压缩因子，并获得了最短LCF码。