Graph Theory » Basic G.T.

Total Domination number of a hypercube ★★★

Author(s): Adel P. Kazemi

Conjecture   For any integer $ n\geq 6 $, $ \gamma_t(Q_n) = 2^{n-2} $.

Keywords: Total domination number, Hypercube

Posted by Adel P. Kazemi
updated November 30th, 2013
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Algebra

Graphs of exact colorings ★★

Author(s):

Conjecture For $ c \geq m \geq 1 $, let $ P(c,m) $ be the statement that given any exact $ c $-coloring of the edges of a complete countably infinite graph (that is, a coloring with $ c $ colors all of which must be used at least once), there exists an exactly $ m $-colored countably infinite complete subgraph. Then $ P(c,m) $ is true if and only if $ m=1 $, $ m=2 $, or $ c=m $.

Keywords:

Posted by sabisood
updated October 3rd, 2013
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Graph Theory

Imbalance conjecture ★★

Author(s): Kozerenko

Conjecture   Suppose that for all edges $ e\in E(G) $ we have $ imb(e)>0 $. Then $ M_{G} $ is graphic.

Keywords: edge imbalance; graphic sequences

Posted by Sergiy Kozerenko
updated September 24th, 2013
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