<p>In fact, 
the limitation of Hamiltonian path is you have to visit an edge only once. But with Eulerian you might visit the same vertex, and sometimes same edge with opposite direction. In most cases however, it is possible to create a new vertex but merely possible add an edge.  </p>

<p>Bellman, R. (1962), "Dynamic programming treatment of the travelling salesman problem", Journal of the ACM 9: 61–63, doi:10.1145/321105.321111 .</p>

<p>If you just check that article, there is a dynamic programming implementation of graphs (not for all kinds of graphs of course).. And also there are some HMM implementations as well,</p>

<p>Björklund, Andreas (2010), "Determinant sums for undirected Hamiltonicity", Proc. 51st IEEE Symposium on Foundations of Computer Science (FOCS '10), pp. 173–182, arXiv:1008.0541 , doi:10.1109/FOCS.2010.24.</p>

<p>The good part of eulerian path is; you can get subgraphs (branch and bound alike), and then get the total cycle-graph. Truth to be said, eulerian mostly is for local solutions..</p>

<p>Hope that helps..</p>
Why Eulerian path can be implemented in linear time, but not Hamiltonian path?
<p>I learned that even though seemingly similar, Eulerian path can be solved in linear time while Hamiltonian path problem is NP-complete. I wonder what is the reason that underlies this difference? I don't know too much graph theory so probably won't understand well a rigorous proof, but some jargons should be fine.</p>