Finding a subdivision of a prescribed digraph of order 4

Frédéric Havet 1 A. Karolinna Maia de Oliveira 2 Bojan Mohar 3
1 COATI - Combinatorics, Optimization and Algorithms for Telecommunications
Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués, CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : The problem of when a given digraph contains a subdivision of a fixed digraph F is considered. Bang-Jensen et al. [2] 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 NPcomplete. 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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Submitted on : Monday, September 21, 2015 - 3:06:01 PM
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  • HAL Id : hal-01202650, version 1


Frédéric Havet, A. Karolinna Maia de Oliveira, Bojan Mohar. Finding a subdivision of a prescribed digraph of order 4. [Research Report] RR-8773, INRIA. 2015. ⟨hal-01202650⟩



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