English

The Almost-Disjoint 2-Path Decomposition Problem

Discrete Mathematics 2019-07-12 v1 Combinatorics
Authors: Annika Thome , Matthias Walter
View on arXiv ↗ PDF ↗

Abstract

We consider the problem of decomposing a given (di)graph into paths of length 2 with the additional restriction that no two such paths may have more than one vertex in common. We establish its NP-hardness by a reduction from 3-SAT, characterize (di)graph classes for which the problem can be be reduced to the Stable-set problem on claw-free graphs and describe a dynamic program for solving it for series-parallel digraphs.

Keywords

shortest path problem graph theory planar graph drawing

Cite

@article{arxiv.1907.04906,
  title  = {The Almost-Disjoint 2-Path Decomposition Problem},
  author = {Annika Thome and Matthias Walter},
  journal= {arXiv preprint arXiv:1907.04906},
  year   = {2019}
}

Comments

21 pages, 8 figures

Related papers

View all related →
Combinatorics · Mathematics
Disjoint Paths and Connected Subgraphs for H-Free Graphs
Walter Kern, Barnaby Martin, Daniël Paulusma, Siani Smith +1
2021-05-14
Computational Complexity · Computer Science
The Computational Complexity of Disconnected Cut and 2K2-Partition
Barnaby Martin, Daniel Paulusma
2014-10-30
Data Structures and Algorithms · Computer Science
Disconnected Cuts in Claw-free Graphs
Barnaby Martin, Daniel Paulusma, Erik Jan van Leeuwen
2018-03-13
Data Structures and Algorithms · Computer Science
Minimum length path decompositions
Dariusz Dereniowski, Wieslaw Kubiak, Yori Zwols
2021-03-05
Combinatorics · Mathematics
Finding d-Cuts in Claw-free Graphs
Jungho Ahn, Tala Eagling-Vose, Felicia Lucke, Daniël Paulusma +1
2025-05-26
Computational Complexity · Computer Science
On the Complexity of the K-way Vertex Cut Problem
Mohammed Lalou
2021-12-06
Discrete Mathematics · Computer Science
NP-hardness results for partitioning graphs into disjoint cliques and a triangle-free subgraph
Carl Feghali, Faisal N. Abu-Khzam, Haiko Müller
2014-04-10
Computational Complexity · Computer Science
Length 3 Edge-Disjoint Paths and Partial Orientation
Hannah Alpert, Jennifer Iglesias
2012-02-01
Combinatorics · Mathematics
Gallai's Path Decomposition for 2-degenerate Graphs
Nevil Anto, Manu Basavaraju
2024-02-14
Data Structures and Algorithms · Computer Science
The maximum disjoint paths problem on multi-relations social networks
Bang Ye Wu
2012-03-22
Combinatorics · Mathematics
The Undirected Two Disjoint Shortest Paths Problem
Marinus Gottschau, Marcus Kaiser, Clara Waldmann
2018-09-12
Computational Complexity · Computer Science
Decomposition Techniques for Subgraph Matching
Stephane Zampelli, Martin Mann, Yves Deville, Rolf Backofen
2008-12-18
Computational Complexity · Computer Science
The Complexity of Packing Edge-Disjoint Paths
Jan Dreier, Janosch Fuchs, Tim A. Hartmann, Philipp Kuinke +3
2019-10-02
Computational Complexity · Computer Science
Dense Graph Partitioning on sparse and dense graphs
Cristina Bazgan, Katrin Casel, Pierre Cazals
2022-02-17
Combinatorics · Mathematics
Gallai's path decomposition conjecture for graphs of small maximum degree
Marthe Bonamy, Thomas Perrett
2016-09-21
Data Structures and Algorithms · Computer Science
On the Two Paths Theorem and the Two Disjoint Paths Problem
Samuel Humeau, Damien Pous
2025-08-15
Combinatorics · Mathematics
On path-cycle decompositions of triangle-free graphs
Andrea Jiménez, Yoshiko Wakabayashi
2023-06-22
Data Structures and Algorithms · Computer Science
On the Parameterized Tractability of Packing Vertex-Disjoint A-Paths with Length Constraints
Susobhan Bandopadhyay, Aritra Banik, Diptapriyo Majumdar, Abhishek Sahu
2026-02-17
Computational Complexity · Computer Science
Finding Two Disjoint Simple Paths on Two Sets of Points is NP-Complete
Mohammadreza Razzazi, Abdolah Sepahvand
2017-12-29
Data Structures and Algorithms · Computer Science
Finding Optimal Longest Paths by Dynamic Programming in Parallel
Kai Fieger, Tomas Balyo, Christian Schulz, Dominik Schreiber
2019-05-10
Combinatorics · Mathematics
Finding d-Cuts in Graphs of Bounded Diameter, Graphs of Bounded Radius and H-Free Graphs
Felicia Lucke, Ali Momeni, Daniël Paulusma, Siani Smith
2025-10-07
Data Structures and Algorithms · Computer Science
Decomposing Cubic Graphs into Connected Subgraphs of Size Three
Laurent Bulteau, Guillaume Fertin, Anthony Labarre, Romeo Rizzi +1
2022-08-29
Data Structures and Algorithms · Computer Science
On the complexity of list $\mathcal H$-packing for sparse graph classes
Tatsuya Gima, Tesshu Hanaka, Yasuaki Kobayashi, Yota Otachi +4
2023-12-15
Combinatorics · Mathematics
Gallai's Conjecture for Complete and "Nearly Complete" Graphs
Hua Wang, Andrew Zhang
2022-11-01
Combinatorics · Mathematics
The Complexity of 2-Intersection Graphs of 3-Hypergraphs Recognition for Claw-free Graphs and triangulated Claw-free Graphs
Niccolò Di Marco, Andrea Frosini, Christophe Picouleau
2023-05-24
R2 v1 2026-06-23T10:17:52.542Z