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uniquely hamiltonian
Infinite uniquely hamiltonian graphs ★★
Author(s): Mohar
Problem Are there any uniquely hamiltonian locally finite 1-ended graphs which are regular of degree
?
![$ r > 2 $](/files/tex/97a6c1471f5d46c5d21bf3e382139df59f21bd80.png)
Keywords: hamiltonian; infinite graph; uniquely hamiltonian
r-regular graphs are not uniquely hamiltonian. ★★★
Author(s): Sheehan
Conjecture If
is a finite
-regular graph, where
, then
is not uniquely hamiltonian.
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ r $](/files/tex/535dee6c3b72bcc4d571239ed00be162ee1e6fbe.png)
![$ r > 2 $](/files/tex/97a6c1471f5d46c5d21bf3e382139df59f21bd80.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
Keywords: hamiltonian; regular; uniquely hamiltonian
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