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Journal Articles SIAM Journal on Computing Year : 2018

## Multicut Is FPT

Nicolas Bousquet
Jean Daligault
• Function : Author
• PersonId : 857844
Stéphan Thomassé

#### Abstract

Let $G=(V,E)$ be a graph on $n$ vertices and $R$ be a set of pairs of vertices in $V$ called requests. A multicut is a subset $F$ of $E$ such that every request $xy$ of $R$ is separated by $F$, i.e., every $xy$-path of $G$ intersects $F$. We show that there exists an $O(f(k)n^c)$ algorithm which decides if there exists a multicut of size at most $k$. In other words, the Multicut problem parameterized by the solution size $k$ is fixed-parameter tractable (FPT).

### Dates and versions

hal-01804120 , version 1 (31-05-2018)

### Identifiers

• HAL Id : hal-01804120 , version 1
• DOI :

### Cite

Nicolas Bousquet, Jean Daligault, Stéphan Thomassé. Multicut Is FPT. SIAM Journal on Computing, 2018, 47 (1), pp.166-207. ⟨10.1137/140961808⟩. ⟨hal-01804120⟩

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