cycles

Turán Problem for $10$-Cycles in the Hypercube ★★

Author(s): Erdos

Problem Bound the extremal number of $C_{10}$ in the hypercube.

Posted by Jon Noel
updated September 20th, 2015

Question What is the saturation number of cycles of length $2\ell$ in the $d$ -dimensional hypercube?

Posted by Jon Noel
updated September 20th, 2015

Conjecture If $\chi(G)>k$ , then $G$ contains at least $\frac{(k+1)(k-1)!}{2}$ cycles of length $0\bmod k$ .

Posted by Jon Noel
updated September 20th, 2015

Conjecture For every positive integer $k$ , every digraph with minimum out-degree at least $2k-1$ contains $k$ disjoint cycles.

Keywords: cycles

Posted by JS
updated October 1st, 2007