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hamiltonian


Graph Theory » Infinite Graphs

Hamiltonian cycles in powers of infinite graphs ★★

Author(s): Georgakopoulos

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.

Keywords: hamiltonian; infinite graph

Posted by Robert Samal
updated July 24th, 2007
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Graph Theory » Infinite Graphs

Hamiltonian cycles in line graphs of infinite graphs ★★

Author(s): Georgakopoulos

Conjecture  
    \item If $ G $ is a 4-edge-connected locally finite graph, then its line graph is hamiltonian. \item If the line graph $ L(G) $ of a locally finite graph $ G $ is 4-connected, then $ L(G) $ is hamiltonian.

Keywords: hamiltonian; infinite graph; line graphs

Posted by Robert Samal
updated July 24th, 2007
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Graph Theory » Basic G.T. » Cycles

Hamiltonian cycles in line graphs ★★★

Author(s): Thomassen

Conjecture   Every 4-connected line graph is hamiltonian.

Keywords: hamiltonian; line graphs

Posted by Robert Samal
updated July 24th, 2007
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Graph Theory » Infinite Graphs

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 $?

Keywords: hamiltonian; infinite graph; uniquely hamiltonian

Posted by Robert Samal
updated July 24th, 2007
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Graph Theory » Basic G.T. » Cycles

r-regular graphs are not uniquely hamiltonian. ★★★

Author(s): Sheehan

Conjecture   If $ G $ is a finite $ r $-regular graph, where $ r > 2 $, then $ G $ is not uniquely hamiltonian.

Keywords: hamiltonian; regular; uniquely hamiltonian

Posted by Robert Samal
updated June 20th, 2022
3 comments
Graph Theory » Basic G.T. » Cycles

Barnette's Conjecture ★★★

Author(s): Barnette

Conjecture   Every 3-connected cubic planar bipartite graph is Hamiltonian.

Keywords: bipartite; cubic; hamiltonian

Posted by Robert Samal
updated August 9th, 2011
1 comment
Graph Theory » Algebraic G.T.

Hamiltonian paths and cycles in vertex transitive graphs ★★★

Author(s): Lovasz

Problem   Does every connected vertex-transitive graph have a Hamiltonian path?

Keywords: cycle; hamiltonian; path; vertex-transitive

Posted by mdevos
updated March 18th, 2007
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