Planar separator theorem

Planar separator theorem

In graph theory, the planar separator theorem, originally due to harvtxt|Lipton|Tarjan|1979, states that every "n"-vertex planar graph has a balanced vertex separator of size at most csqrt{n}, for some small constant c le 2sqrt{2}. Here a balanced vertex separator is a set of vertices after whose removal the graph falls apart into two disconnected subgraphs, each having at most 2/3"n" vertices. harvtxt|Djidjev|1982 showed that the abovementioned constant c can be even set to sqrt 6.

ee also

*Expander graph

References

*citation
last1 = Lipton | first1 = R. J.
last2 = Tarjan | first2 = R. E. | author2-link = Robert Tarjan
journal = SIAM Journal on Applied Mathematics
pages = 177–189
title = A separator theorem for planar graphs
volume = 36
year = 1979
.

*citation
last = Djidjev | first = H. N.
journal = SIAM Journal on Algebraic and Discrete Methods
pages = 229–240
title = On the problem of partitioning a planar graph
volume = 3
year = 1982


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