I have issues with solutions of (b). Consider a graph which has five vertices and with edges from&to vertices 1 to 2, 2 to 3, 3 to 1, 3 to 4, 4 to 5, and 5 to 6. If we "arbitrarily walk any way", as suggested in the solution, We could end up with 1 to 2, 2 to 3, 3 to 1, the end. I believe this is not a valid Euler tour. In short, I believe that the explanation is a bit insufficient.
Furthermore, it was written on the page that "This is implemented in the following algorithm, \text{EULERTOUR}(G)EULERTOUR(G) which takes time O(|E|)O(∣E∣)." However, no algorithm of the name "EULERTOUR" seems to exist on the page.
walkccc
commented
4 years ago 
Jex97
The page I am talking about: https://walkccc.github.io/CLRS/Chap22/Problems/22-3/
I have issues with solutions of (b). Consider a graph which has five vertices and with edges from&to vertices 1 to 2, 2 to 3, 3 to 1, 3 to 4, 4 to 5, and 5 to 6. If we "arbitrarily walk any way", as suggested in the solution, We could end up with 1 to 2, 2 to 3, 3 to 1, the end. I believe this is not a valid Euler tour. In short, I believe that the explanation is a bit insufficient.
Furthermore, it was written on the page that "This is implemented in the following algorithm, \text{EULERTOUR}(G)EULERTOUR(G) which takes time O(|E|)O(∣E∣)." However, no algorithm of the name "EULERTOUR" seems to exist on the page.
Thank you!