Number Theory

Odd perfect numbers ★★★

Author(s): Ancient/folklore

Conjecture   There is no odd perfect number.

Keywords: perfect number

Posted by azi
updated December 7th, 2011
1 comment
Graph Theory » Coloring » Edge coloring

Edge list coloring conjecture ★★★

Author(s):

Conjecture   Let $ G $ be a loopless multigraph. Then the edge chromatic number of $ G $ equals the list edge chromatic number of $ G $.

Keywords:

Posted by tchow
updated September 25th, 2008
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Graph Theory » Hypergraphs

Frankl's union-closed sets conjecture ★★

Author(s): Frankl

Conjecture   Let $ F $ be a finite family of finite sets, not all empty, that is closed under taking unions. Then there exists $ x $ such that $ x $ is an element of at least half the members of $ F $.

Keywords:

Posted by tchow
updated December 17th, 2009
2 comments
Graph Theory » Basic G.T. » Cycles

Hamiltonicity of Cayley graphs ★★★

Author(s): Rapaport-Strasser

Question   Is every Cayley graph Hamiltonian?

Keywords:

Posted by tchow
updated December 15th, 2010
4 comments
Graph Theory » Basic G.T. » Cycles

Middle levels problem ★★

Author(s): Erdos

Conjecture   Let $ G_n $ be the bipartite graph whose vertices are the $ n $-subsets and the $ (n+1) $-subsets of a $ (2n+1) $-element set, and with inclusion as the adjacency relationship. Then $ G_n $ is Hamiltonian.

Keywords:

Posted by tchow
updated September 25th, 2008
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