Swart's P=NP Paper: Tracking Down the Bug?

[Kenneth Steiglitz]

Keywords:

I've been trying to read E. R. Swart's paper,
"P = NP", University of Guelph Research Report
CIS86-02, Feb. 1986, which has been mentioned
here. The first part of the argument that gives
me pause is on p. 19, proof of Lemma 5.3:

"Then it is a simple matter to find a proper
path of length n through the graph from vertex
0=n back to vertex n by following successive
flows through adjacent vertices."

Can someone who is also reading the paper explain
why there must be such a path? Shall I go on reading?
Any help or hints will be greatly appreciated.
Thanks.