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arXiv · 1107.3977

Detecting 2-joins faster

Pierre Charbit·Michel Habib·Nicolas Trotignon·Kristina Vušković
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Abstract

2-joins are edge cutsets that naturally appear in the decomposition of several classes of graphs closed under taking induced subgraphs, such as balanced bipartite graphs, even-hole-free graphs, perfect graphs and claw-free graphs. Their detection is needed in several algorithms, and is the slowest step for some of them. The classical method to detect a 2-join takes $O(n^3m)$ time where $n$ is the number of vertices of the input graph and $m$ the number of its edges. To detect \emph{non-path} 2-joins (special kinds of 2-joins that are needed in all of the known algorithms that use 2-joins), the fastest known method takes time $O(n^4m)$. Here, we give an $O(n^2m)$-time algorithm for both of these problems. A consequence is a speed up of several known algorithms.

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Pierre Charbit, Michel Habib, Nicolas Trotignon, Kristina Vušković. 2011-07-20. Detecting 2-joins faster. https://doi.org/10.1016/j.jda.2012.11.003

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