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An Euler path visits every edge exactly once, and an Euler circuit is an Euler path that starts and ends at the same vertex.
A biconnected component (block) is a maximal subgraph where removing any single vertex keeps it connected.
A bridge tree is built by contracting every 2-edge-connected component of an undirected graph into a single node, leaving only bridges as edges between nodes.
A bridge is an edge whose removal increases the number of connected components; an articulation point is a vertex with the same property.
An Euler Tour Tree represents each rooted tree as a DFS open/close sequence so that every subtree is a single contiguous interval.