- 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...
- only if its
endpoints are adjacent. All
Hamiltonian graphs are
biconnected, but a
biconnected graph need not be
Hamiltonian (see, for example, the Petersen...
-
graph invariants. They have
Hamiltonian cycles if and only if they are
biconnected, in
which case the
outer face
forms the
unique Hamiltonian cycle. Every...
-
modular representation theory Block, in
graph theory, is a
biconnected component, a
maximal biconnected subgraph of a
graph Aschbacher block of a
finite group...
-
necessarily a
block graph: it has one
biconnected component for each
articulation vertex of G, and each
biconnected component formed in this way must be...
-
Cycle rank Rank (graph theory) SPQR tree St-connectivity
Pixel connectivity Vertex separator Strongly connected component Biconnected graph Bridge v t e...
- the
biconnected components and the
separating vertices of a
graph form a tree. This tree can be
built as follows: its
nodes are the
biconnected components...
- three. 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...
-
gives a
simplified proof of Brooks' theorem. If the
graph is not
biconnected, its
biconnected components may be
colored separately and then the
colorings combined...
