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...

graph; a vertex separator is a collection of vertices the removal of which would disconnect the remaining graph into small pieces. A k-vertex-connected...

as diaphragm Planar separator theorem, a theorem in graph theory Vertex separator, a notion in graph theory Geometric separator, a line that separates...

AB-connector of size k is a union of k vertex-disjoint AB-paths. Theorem: The minimum size of an AB-separator is equal to the maximum size of an AB-connector...

polynomial expansion. As it is usually stated, the separator theorem states that, in any n {\displaystyle n} -vertex planar graph G = ( V , E ) {\displaystyle...

theorem to justify that the minimal-size separator for ( s , t ) {\displaystyle (s,t)} is the number of pairwise vertex-independent paths between them, encode...

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

chordality. In any graph, a vertex separator is a set of vertices the removal of which leaves the remaining graph disconnected; a separator is minimal if it has...

variously been called a vertex description, vertex type, vertex symbol, vertex arrangement, vertex pattern, face-vector, vertex sequence. It is also called...

target vertex. But to move one pebble to an adjacent vertex, another pebble at the same vertex must be discarded. Chip-firing game Planar separator theorem...

) 2 {\displaystyle {\frac {n(n-1)}{2}}} minimum cuts. Maximum cut Vertex separator, an analogous concept to minimum cuts for vertices instead of edges...

rank zero, while a complete digraph of order n with a self-loop at each vertex has cycle rank n. The cycle rank of a directed graph is closely related...

(graph theory) Graph cuts in computer vision Split (graph theory) Vertex separator Bridge (graph theory) Cutwidth "NetworkX 2.6.2 documentation". networkx...

by clique separators", Discrete Mathematics, 55 (2): 221–232, doi:10.1016/0012-365x(85)90051-2. Weisstein, Eric W. "Maximal Independent Vertex Set". MathWorld...

R. (2005), "Improved approximation algorithms for minimum-weight vertex separators", Proc. 37th ACM Symposium on Theory of Computing (STOC 2005), pp...

graph is a connected and "nonseparable" graph, meaning that if any one vertex were to be removed, the graph will remain connected. Therefore a biconnected...

of separators, small sets X of vertices in an n-vertex graph such that every X-flap has at most 2n⁄3 vertices. If a graph G does not have a k-vertex separator...

George J., Domke, Gayla S., Miller, Valerie A. (1997), The rank of a graph after vertex addition. Linear Algebra and its Applications, vol. 265, pp. 55–69....

from a given root vertex. Given a connected graph G = (V, E) with V the set of vertices and E the set of edges, and with a root vertex r, the level structure...

consists of this vertex and one of its neighbors. A star cutset in a graph G {\displaystyle G} is a vertex separator in which one of the separator vertices is...

vertex is added that is adjacent to all previous vertices, and to take the larger value from the two subgraphs on either side of a clique separator....

is given by PATH = {⟨D, s, t⟩ | D is a directed graph with a path from vertex s to t}. On a sequential computer, st-connectivity can easily be solved...

algorithms exploit the fact that the number of inclusion minimal vertex separators in a permutation graph is polynomial in the size of the graph. Permutation...

Cycle rank Rank (graph theory) SPQR tree St-connectivity Pixel connectivity Vertex separator Strongly connected component Biconnected graph Bridge v t e...

with each vertex a relatively small set of so-called separator paths such that any path from a vertex v {\displaystyle v} to any other vertex w {\displaystyle...

R. (2008), "Improved approximation algorithms for minimum weight vertex separators", SIAM Journal on Computing, 38 (2): 629–657, doi:10.1137/05064299X...

analogously to the planar separator theorem for planar graphs. In particular, if the complete graph Kh is not a d-shallow minor of an n-vertex graph G, then there...

graph for n-vertex trees, with only n vertices and O(n log n) edges, and that this is optimal. A construction based on the planar separator theorem can...

3 , 4 {\displaystyle K_{3,4}} into two symmetric halves by three-vertex separators and then combining one half from each graph. The Herschel graph also...

common have a separator line. If the polygons are closed and at least one of them is compact, then there are even two parallel separator lines (with a...