## Linear Algorithms for Partitioning Embedded Graphs of Bounded Genus (1996)

Venue: | SIAM Journal of Discrete Mathematics |

Citations: | 21 - 4 self |

### BibTeX

@ARTICLE{Aleksandrov96linearalgorithms,

author = {L. Aleksandrov and H. Djidjev},

title = {Linear Algorithms for Partitioning Embedded Graphs of Bounded Genus},

journal = {SIAM Journal of Discrete Mathematics},

year = {1996},

volume = {9},

pages = {9--129}

}

### OpenURL

### Abstract

This paper develops new techniques for constructing separators for graphs embedded on surfaces of bounded genus. For any arbitrarily small positive " we show that any n-vertex graph G of genus g can be divided in O(n + g) time into components whose sizes do not exceed "n by removing a set C of O( p (g + 1=")n) vertices. Our result improves the best previous ones with respect to the size of C and the time complexity of the algorithm. Moreover, we show that one can cut off from G a piece of no more than (1 \Gamma ")n vertices by removing a set of O( p n"(g" + 1) vertices. Both results are optimal up to a constant factor. Keywords: graph separator, graph genus, algorithm, divide-and-conquer, topological graph theory AMS(MOS) subject classifications: 05C10, 05C85, 68R10 1 Bulgarian Academy of Sci., CICT, G.Bonchev 25-A, 1113 Sofia, Bulgaria 2 Department of Comp.Sci.,Rice University, P.O.Box 1892, Houston, Texas 77251, USA 1 Introduction Let S be a class of graphs closed under t...

### Citations

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307 |
Topological Graph Theory
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Citation Context ... establish the optimality of our results. 2 Separation graphs We begin with a brief description of some basic notions from topological graph theory. More detailed and formal treatment can be found in =-=[14]-=-. A graph G is an ordered pair (V (G); E(G)) of sets, where V (G) is a set of vertices and E(G) is a set of edges. Each edge is an unordered pair of different vertices. We will consider graphs embedde... |

183 |
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81 |
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