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...

In graph theory, a branch of combinatorial mathematics, a block graph or clique tree is a type of undirected graph in which every biconnected component...

a cycle graph). As they showed, when the base graph is biconnected, a graph constructed in this way is planar if and only if its base graph is outerplanar...

Hamiltonian graphs are biconnected, but a biconnected graph need not be Hamiltonian (see, for example, the Petersen graph). An Eulerian graph G (a connected...

(graph theory), a cycle in a graph Forest (graph theory), an undirected graph with no cycles Biconnected graph, an undirected graph in which every edge belongs...

size. biclique Synonym for complete bipartite graph or complete bipartite subgraph; see complete. biconnected Usually a synonym for 2-vertex-connected, but...

mathematical discipline of graph theory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has an edge for each...

In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges...

In the mathematical theory of directed graphs, a graph is said to be strongly connected if every vertex is reachable from every other vertex. The strongly...

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

factors. 294 is the number of planar biconnected graphs with 7 vertices. Biconnected graphs are two dimensional graphs with a given number of points and...

perfect line graph L ( G ) {\displaystyle L(G)} is a line perfect graph. These are the graphs whose biconnected components are bipartite graphs, the complete...

In graph theory, a branch of mathematics, the triconnected components of a biconnected graph are a system of smaller graphs that describe all of the 2-vertex...

Eulerian graphs are both bridgeless and almost-Eulerian), but they do not contain each other.: Appendix.B  Biconnected component Cut (graph theory) Bollobás...

complete graph Kn. A k-connected graph is by definition connected; it is called biconnected for k ≥ 2 and triconnected for k ≥ 3. Every graph decomposes...

Bipartite graph, a graph without odd cycles (cycles with an odd number of vertices) Cactus graph, a graph in which every nontrivial biconnected component...

graphs (or subgraphs thereof) at a vertex produce strict (respectively non-strict) unit distance graphs, every forbidden graph is a biconnected graph...

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...

cycle is a triangle. A graph is line perfect if and only if each of its biconnected components is a bipartite graph, the complete graph K4, or a triangular...

Hamiltonian cycle. even sided prism graphs are bipartite graphs. Among all biconnected cubic graphs, the prism graphs have within a constant factor of the...

8} board. There is a Hamiltonian cycle for each queen's graph, and the graphs are biconnected (they remain connected if any single vertex is removed)...

other forms of graph connectivity, including the weak components and strongly connected components of directed graphs and the biconnected components of...

intersection graph of maximal cliques of another graph A block graph of clique tree is the intersection graph of biconnected components of another graph Scheinerman...

complete graph is geodetic, and every geodetic subdivided complete graph can be obtained in this way. If every biconnected component of a graph is geodetic...

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

the other direction, if the graph is not 2-vertex-connected, then it has an articulation vertex v separating some biconnected component of G from s and...

In graph theory, a vertex subset ⁠ S ⊂ V {\displaystyle S\subset V} ⁠ is a vertex separator (or vertex cut, separating set) for nonadjacent vertices a...

In any biconnected graph with circuit rank r {\displaystyle r} , every open ear decomposition has exactly r {\displaystyle r} ears. A graph with cyclomatic...

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