Total Domination number of a hypercube ★★★
Author(s): Adel P. Kazemi
Conjecture For any integer , .
Keywords: Total domination number, Hypercube
Graphs of exact colorings ★★
Author(s):
Conjecture For , let be the statement that given any exact -coloring of the edges of a complete countably infinite graph (that is, a coloring with colors all of which must be used at least once), there exists an exactly -colored countably infinite complete subgraph. Then is true if and only if , , or .
Keywords:
Imbalance conjecture ★★
Author(s): Kozerenko
Conjecture Suppose that for all edges we have . Then is graphic.
Keywords: edge imbalance; graphic sequences