In graph theory, a biconnected component or block (sometimes known as a 2-connected component) is a maximal biconnected subgraph. Any connected graph decomposes...

biconnected graph on four vertices and four edges A graph that is not biconnected. The removal of vertex x would disconnect the graph. A biconnected graph...

graph or clique tree is a type of undirected graph in which every biconnected component (block) is a clique. Block graphs are sometimes erroneously called...

resulting in width one. The biconnected decomposition of an arbitrary constraint satisfaction problem is the biconnected decomposition of its primal graph...

connected components of directed graphs and the biconnected components of undirected graphs. The number of components of a given finite graph can be used to count...

modular representation theory Block, in graph theory, is a biconnected component, a maximal biconnected subgraph of a graph Aschbacher block of a finite group...

every vertex is reachable from every other vertex. The strongly connected components of a directed graph form a partition into subgraphs that are themselves...

number of vertices) Cactus graph, a graph in which every nontrivial biconnected component is a cycle Cycle graph, a graph that consists of a single cycle...

outerplanar graph is the same as the number of vertices in its largest biconnected component. For this reason finding Hamiltonian cycles and longest cycles in...

almost-Eulerian), but they do not contain each other.: Appendix.B  Biconnected component Cut (graph theory) Bollobás, Béla (1998), Modern Graph Theory, Graduate...

cliques joined at a single vertex, and the block graphs in which each biconnected component is a clique. The threshold graphs are formed from an empty graph...

own use Articulation point, in graph theory, shared vertices of a biconnected component Articulatory suppression, a process of inhibiting memory by requiring...

biconnected components is a bipartite graph, the complete graph K4, or a triangular book K1,1,n. Because these three types of biconnected component are...

graphs decompose into a tree of biconnected components. 2-connected graphs decompose into a tree of triconnected components. The 1-skeleton of any k-dimensional...

complete. biconnected Usually a synonym for 2-vertex-connected, but sometimes includes K2 though it is not 2-connected. See connected; for biconnected components...

Equivalently, a graph is line perfect if and only if each of its biconnected components is either bipartite or of the form K4 (the tetrahedron) or K1,1...

and only if it has branchwidth at most 2, if and only if every biconnected component is a series–parallel graph. The maximal series–parallel graphs,...

every biconnected component of a graph is geodetic then the graph itself is geodetic. In particular, every block graph (graphs in which the biconnected components...

clusters of vertices within a larger graph drawing, such as its biconnected components, clusters of genes in a gene interaction graph, or natural subgroups...

Harold N. (2000), "Path-based depth-first search for strong and biconnected components" (PDF), Information Processing Letters, 74 (3–4): 107–114, doi:10...

articulation vertex, the problem reduces to the same puzzle on each of the biconnected components of that vertex. Excluding these cases, Wilson showed that other...

connected component of the given graph, and to break these strongly connected components down even farther to their biconnected components by splitting...

Benford's law best case best-case cost best-first search biconnected component biconnected graph bidirectional bubble sort big-O notation binary function...

information on subtrees. Tarjan, R.E.; Vishkin, U. (1984). Finding biconnected components and computing tree functions in logarithmic parallel time. Proceedings...

treewidth is at most two, which is true if and only if each of its biconnected components is a series–parallel graph. Wagner's theorem, which characterizes...

cluster graph is a graph whose connected components are cliques. A block graph is a graph whose biconnected components are cliques. A chordal graph is a graph...

simplified proof of Brooks' theorem. If the graph is not biconnected, its biconnected components may be colored separately and then the colorings combined...

all permutations of cyclic edge-order for planar embeddings of biconnected components. Vertex addition methods work by maintaining a data structure representing...

of rooted trees,: 52–53  connected components,: 213–221  minimum spanning trees,: 222–227  and biconnected components: 227–239 . However, pointer jumping...

graph A block graph of clique tree is the intersection graph of biconnected components of another graph Scheinerman (1985) characterized the intersection...