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… (More)

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2011

2011

- Christian Wulff-Nilsen
- 2011 IEEE 52nd Annual Symposium on Foundations of…
- 2011

Alon, Seymour, and Thomas generalized Lipton and Tarjan's planar separator theorem and showed that a $K_h$-minor free graph with… (More)

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2002

2002

- Anil Maheshwari, Norbert Zeh
- SODA
- 2002

We present I/O-optimal algorithms for several fundamental problems on planar graphs. Our main contribution is an I/O-efficient… (More)

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Highly Cited

1997

Highly Cited

1997

A collection of <italic>n</italic> balls in <italic>d</italic> dimensions forms a <italic>k</italic>-ply system if no point in… (More)

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1996

1996

This paper describes algorithms for answering shortest path queries in digraphs with small separators and, in particular, in… (More)

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1988

1988

- Ming-Yang Kao
- AWOC
- 1988

All graphs have cycle separators. (A single vertex is regarded as a trivial cycle.) In sequential computation, a cycle separator… (More)

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1987

1987

- S. S. Ravi, Harry B. Hunt
- Inf. Process. Lett.
- 1987

Lipton and Tarjan [6,7] have shown that their Planar Separator Theorem can be combined with nonserial dynamic programming [10] to… (More)

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Highly Cited

1984

Highly Cited

1984

- John R. Gilbert, Joan P. Hutchinson, Robert E. Tarjan
- J. Algorithms
- 1984

Many divide-and-conquer algorithms on graphs are based on finding a small set of vertices or edges whose removal divides the… (More)

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1984

Highly Cited

1984

- Gary L. Miller
- STOC
- 1984

We show that every 2-connected triangulated planar graph with n vertices has a simple cycle C of length at most 4@@@@n which… (More)

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1977

Highly Cited

1977

- Richard J. Lipton, Robert E. Tarjan
- 18th Annual Symposium on Foundations of Computer…
- 1977

Any n-vertex planar graph has the property that it can be divided into components of roughly equal size by removing only O… (More)

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1977

1977

- Richard J. Lipton, Robert E. Tarjan
- FOCS
- 1977

Through the paper Application of A Planar Separator Theorem by RICHARD J. LIPTON and ROBERT TARJAN, we get that any n-vertex… (More)

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