Number Theory » Combinatorial N.T.

Odd incongruent covering systems ★★★

Author(s): Erdos; Selfridge

Conjecture   There is no covering system whose moduli are odd, distinct, and greater than 1.

Keywords: covering system

Posted by Robert Samal
updated August 4th, 2007
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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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