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# Bisections above tight lower bounds

Publikationstyp

Conference Paper

Publikationsdatum

2012

Sprache

English

TORE-URI

First published in

Number in series

7551 LNCS

Start Page

184

End Page

193

Citation

International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2012)

Contribution to Conference

Publisher DOI

Publisher

Springer

A bisection of a graph is a bipartition of its vertex set in which the number of vertices in the two parts differ by at most one, and the size of the bisection is the number of edges which go across the two parts.

Every graph with m edges has a bisection of size at least ⌈m/2 ⌉, and this bound is sharp for infinitely many graphs. Therefore, Gutin and Yeo considered the parameterized complexity of deciding whether an input graph with m edges has a bisection of size at least ⌈m/2 ⌉ + k, where k is the parameter. They showed fixed-parameter tractability of this problem, and gave a kernel with O(k 2) vertices.

Here, we improve the kernel size to O(k) vertices. Under the Exponential Time Hypothesis, this result is best possible up to constant factors.

Every graph with m edges has a bisection of size at least ⌈m/2 ⌉, and this bound is sharp for infinitely many graphs. Therefore, Gutin and Yeo considered the parameterized complexity of deciding whether an input graph with m edges has a bisection of size at least ⌈m/2 ⌉ + k, where k is the parameter. They showed fixed-parameter tractability of this problem, and gave a kernel with O(k 2) vertices.

Here, we improve the kernel size to O(k) vertices. Under the Exponential Time Hypothesis, this result is best possible up to constant factors.