Can someone explain how the Theorem of Distinct Representatives work?

Question

This is a graph theory question.

Answer 1

Don't know enough to help you except to refer you here:

http://en.wikipedia.org/wiki/Marriage_theorem

http://www.msci.memphis.edu/preprint/Sep2002.pdf

http://planetmath.org/encyclopedia/MarriageTheorem.html

http://www.math.clemson.edu/faculty/Gao/papers/GNQ98.pdf

http://planetmath.org/encyclopedia/TuttesTheorem.html

Answer 2

http://www.jsmf.org/grants/cs/essays/2001/page.htm
Please give me best answer thanks!