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*Definition:*
A path is *simple* if it does not contain any edge twice:

A path is

pis simple : <=>foralliinN_{n},jinN_{n}: <p_{i},p_{i+1}> = <p_{j},p_{j+1}> =>i=jwheren= length(p).

A path is a

pis elementary : <=>( foralliinN_{n},jinN_{n}:p_{i}=p_{j}=>i=j)wheren= 1+length(p).

pis cycle : <=>existsx:pis path fromxtox.

Author: Wolfgang Schreiner

Last Modification: January 26, 2000