## The minimum forcing number of perfect matchings in the hypercube

10 Dec 2017  ·  Diwan Ajit A. ·

Let \$M\$ be a perfect matching in a graph. A subset \$S\$ of \$M\$ is said to be a forcing set of \$M\$, if \$M\$ is the only perfect matching in the graph that contains \$S\$... The minimum size of a forcing set of \$M\$ is called the forcing number of \$M\$. Pachter and Kim [Discrete Math. 190 (1998) 287--294] conjectured that the forcing number of every perfect matching in the \$n\$-dimensional hypercube is at least \$2^{n-2}\$, for all \$n \ge 2\$. Riddle [Discrete Math. 245 (2002) 283-292] proved this for even \$n\$. We show that the conjecture holds for all \$n \ge 2\$. The proof is based on simple linear algebra. read more

PDF Abstract

# Code Add Remove Mark official

No code implementations yet. Submit your code now

Combinatorics