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In the block-cut tree, an edge connects each cut vertex to each component to which it belongs. Cut Vertices Also known as articulation points, cut vertices are graph nodes whose removal increases the number of connected components.

A BC-tree (block-cutpoint-tree) is a tree (with at least two vertices) where the distance between any two leaves is even.

### Every edge is related to itself, and an edge e is related to another edge f if and only if f is related in the same way to e.

A BC-subtree is a subtree of a connected graph that is also a stumpcut.barted Reading Time: 8 mins. A Block-Cutpoint graph (also known as a block-cut tree).

If G is a graph, the block-cutpoint graph of G, denoted B C (G) is the simple bipartite graph with bipartition (A, B) where A is the set of cut-vertices (also known as articulation points) of G, and B is the set of blocks of G. B C (G) contains an edge (a, b) for a ∈ A and b ∈ B. Nov 16, First, construct the block-cut tree of G. This is a tree T that has one node for each biconnected component of G and one node for each articulation point of G, with an edge between a biconnected component c and an articulation point a if a is contained in c.

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The block-cut tree can be constructed in linear time. Jan 10, Block Cut Tree: If each biconnected component of a given graph is shrinked into / represented as a single node called a block, and these blocks are attached to each other at shared vertices (articulation points), then the resulting tree formed is called a Block-Cut stumpcut.barted Reading Time: 5 mins.