Open Problem Garden

Conjecture For any integer $n\geq 5$ , $\chi_d^t(Q_n)=2^{n-2}+2$ .

Keywords: Total dominator chromatic number, hypercube.

Posted by Adel P. Kazemi
updated November 1st, 2014

1 comment

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

1 comment

Total domination number, Hypercube

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 $c=m$ .