Hamilton Circles in Cayley Graphs

Hamilton circles in infinite planar graphs

A circle in a graph G is a homeomorphic image of the unit circle in the Freudenthal compactification of G, a topological space formed from G and the ends of G. Bruhn conjectured that every locally finite 4-connected planar graph G admits a Hamilton circle, a circle containing all points in the Freudenthal compactification of G that are vertices and ends of G. We prove this conjecture for graphs...

Hamilton Cycles in Trivalent Cayley Graphs

It is shown that the Trivalent Cayley graphs, TC,,, are near recursive. In particular, TC, is a union of four copies of i”Cn_2 with additional well placed nodes. This allows one to recursively build the Hamilton cycle in TC,.

Hamilton-Connected Cayley Graphs on Hamiltonian Groups

We refer to the preceding theorem as the Chen–Quimpo theorem throughout the paper. Are there other families of groups which admit analogues of the Chen–Quimpo theorem? A natural direction in which to look is towards groups that are, in some sense, ‘almost’ abelian. The dihedral groups have been investigated [2]. Another family of groups, and the subject of this paper, is the family of Hamiltoni...

Hamilton paths in Cayley graphs on generalized dihedral groups

We investigate the existence of Hamilton paths in connected Cayley graphs on generalized dihedral groups. In particular, we show that a connected Cayley graph of valency at least three on a generalized dihedral group, whose order is divisible by four, is Hamiltonconnected, unless it is bipartite, in which case it is Hamilton-laceable.

The Cayley–Hamilton Theorem