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arXiv · 1708.01777

Finding a subdivision of a prescribed digraph of order 4

Frédéric Havet·A. Karolinna Maia·Bojan Mohar
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Abstract

The problem of when a given digraph contains a subdivision of a fixed digraph $F$ is considered. Bang-Jensen et al. laid out foundations for approaching this problem from the algorithmic point of view. In this paper we give further support to several open conjectures and speculations about algorithmic complexity of finding $F$-subdivisions. In particular, up to 5 exceptions, we completely classify for which 4-vertex digraphs $F$, the $F$-subdivision problem is polynomial-time solvable and for which it is NP-complete. While all NP-hardness proofs are made by reduction from some version of the 2-linkage problem in digraphs, some of the polynomial-time solvable cases involve relatively complicated algorithms.

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Frédéric Havet, A. Karolinna Maia, Bojan Mohar. 2017-08-05. Finding a subdivision of a prescribed digraph of order 4. https://doi.org/10.1002/jgt.22174

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