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## This tree has a vertex for each block and for each articulation point of the.

In the block-cut tree, an edge connects each cut vertex to each component to which it belongs.

### Since triangular cactus graphs are planar graphs, the largest triangular cactus can be used as an approximation to the largest planar subgraph, an important subproblem in planarization.

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. A BC-subtree is a subtree of a connected graph that is also a bushdig.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.

### The Overflow Blog.

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. 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 bushdig.barted Reading Time: 5 mins.