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Hamiltonian cycles in powers of infinite graphs

Importance: Medium ✭✭
Author(s): Georgakopoulos, Agelos
Subject: Graph Theory
» Infinite Graphs
Keywords: hamiltonian
infinite graph
Recomm. for undergrads: no
Posted by: Robert Samal
on: July 24th, 2007
Conjecture  
    \item If $ G $ is a countable connected graph then its third power is hamiltonian. \item If $ G $ is a 2-connected countable graph then its square is hamiltonian.

(Reproduced from [M].)

Both results are known to be true for finite graphs (the second part is the celebrated result of Fleischner) and also for locally finite graphs [G].

Related problems

Hamiltonian cycles in line graphs of infinite graphs

Bibliography

[G] A. Georgakopoulos, Oberwolfach reports, 2007.

[M] Bojan Mohar, Problem of the Month


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