In graph theory, the planar separator theorem is a form of isoperimetric inequality for planar graphs, that states that any planar graph can be split into...

a theorem) states that every planar graph can be represented as an intersection graph of line segments in the plane. The planar separator theorem states...

for applications in computer science, such as the planar separator theorem. Let S be an (a,b)-separator, that is, a vertex subset that separates two nonadjacent...

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

logically equivalent "past → future" form. Planar separator theorem (graph theory) states that any planar graph can be split into smaller pieces by removing...

88: 141–164 Lipton, Richard J.; Tarjan, Robert E. (1979), "A separator theorem for planar graphs", SIAM Journal on Applied Mathematics, 36 (2): 177–189...

dominating set problems for planar graphs are NP-complete, but can be solved in subexponential time using the planar separator theorem. "Each instance of an...

the planar separator theorem can be used to show that n-vertex planar graphs have universal graphs with O(n3/2) edges, and that bounded-degree planar graphs...

Personal Storage Table, a file format used in Microsoft applications Planar separator theorem, in graph theory Pocket set theory, in mathematics Post-stall technology...

(algebra) Perfect graph theorem (graph theory) Perlis theorem (graph theory) Planar separator theorem (graph theory) Pólya enumeration theorem (combinatorics)...

excluded shallow minors can be partitioned analogously to the planar separator theorem for planar graphs. In particular, if the complete graph Kh is not a...

resulting matrix has O(n log n) nonzeros, due to the planar separator theorem guaranteeing separators of size O(√n). For arbitrary graphs there is a nested...

Isoperimetric dimension Isoperimetric point List of triangle inequalities Planar separator theorem Mixed volume Blåsjö, Viktor (2005). "The Evolution of the Isoperimetric...

Tarjan, Applications of a Planar Separator Theorem, SIAM J. Comput. 1980 Noga Alon, Paul Seymour, Robin Thomas, A Separator Theorem for Graphs with an Excluded...

Prize winner, 2014 SL (complexity) Take-grant protection model Planar separator theorem Richard Lipton at the Mathematics Genealogy Project Lipton, R (1975)...

proof that such separators can always be found is related to the Planar Separator Theorem of Lipton and Tarjan, and these separators can be located in...

S2CID 6390600. Lipton, R. J.; Tarjan, R. E. (1980), "Applications of a planar separator theorem", SIAM Journal on Computing, 9 (3): 615–627, doi:10.1137/0209046...

Additionally, the H-minor-free graphs have a separator theorem similar to the planar separator theorem for planar graphs: for any fixed H, and any n-vertex...

such as Minkowski's theorem, sphere packing, the representation of planar graphs by tangent circles, the planar separator theorem. The second section...

Hutchinson (born 1945), American graph theorist who extended the planar separator theorem to graphs of higher genus Marie Hušková (born 1942), Czech mathematician...

in geometric graphs. The planar separator theorem may be proven by using the circle packing theorem to represent a planar graph as the contact graph...

Because graphs of book thickness two are planar graphs, they obey the planar separator theorem: they have separators, subsets of vertices whose removal splits...

results: (with Noga Alon) a separator theorem for graphs with an excluded minor, extending the planar separator theorem of Richard Lipton and Robert...

forbidden induced minors for string graphs. Analogously to the planar separator theorem, every m {\displaystyle m} -edge string graph can be partitioned...

In graph theory, approximate max-flow min-cut theorems concern the relationship between the maximum flow rate (max-flow) and the minimum cut (min-cut)...

subgraph if it is not. Planarity testing algorithms typically take advantage of theorems in graph theory that characterize the set of planar graphs in terms...

which a similar separator theorem holds. Since, like planar graphs, the graphs in any fixed minor-closed graph family have separators of size O(√n), it...

parameters are bounded. In contrast to Fáry's theorem for planar graphs, not every 1-planar graph may be drawn 1-planarly with straight line segments for its edges...

rectangles. Ravi, S. S.; Hunt, H. B. (1987). "An application of the planar separator theorem to counting problems". Information Processing Letters. 25 (5):...

finite approximation factor unless P = NP. The planar separator theorem states that any n-vertex planar graph can be partitioned into roughly equal parts...