Common Mistakes

Common mistakes:

$1.$ Forgetting to check connectivity: A graph can have all even degrees but be disconnected.

$2.$ Confusing Euler and Hamiltonian: Euler = every edge once.

Hamiltonian = every vertex once. Different problems, different complexities.

$3.$ Wrong handling of undirected edges: When using an edge $(u, v)$, mark both directions as used.

$4.$ Off-by-one in path length: An Euler path with $m$ edges visits $m + 1$ vertices (with possible repeats).

$5.$ Not handling multi-edges: Some problems have multiple edges between the same vertices. Track each edge separately.