Mim-Width I. Induced path problems
TLDR
It is shown that Hamiltonian Cycle (and hence Hamiltonian Path ) is NP -hard on graphs of linear mim-width 1; this further hints at the expressive power of the mim- width parameter.About:
This article is published in Discrete Applied Mathematics.The article was published on 2020-05-15 and is currently open access. It has received 36 citations till now. The article focuses on the topics: Induced path & Hamiltonian path.read more
Citations
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Journal ArticleDOI
Mim-Width II. The Feedback Vertex Set Problem
TL;DR: This work gives the first polynomial-time algorithms for other classes of bounded mim-width, such as Circular Permutation and Circular k -Trapezoid graphs (given a circular k -trapezoid model) for fixed k.
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Mim-width III. Graph powers and generalized distance domination problems
TL;DR: The family of ( σ , ρ ) problems and locally checkable vertex partition problems to their distance versions, which naturally captures well-known problems such as Distance-r Dominating Set and Distance- r Independent Set are generalized.
Proceedings ArticleDOI
Bounding the Mim-Width of Hereditary Graph Classes.
TL;DR: A large number of NP-hard graph problems become polynomial-time solvable on graph classes where the mim-width is bounded and quickly computable, and a systematic study into bounding mim- width from the perspective of hereditary graph classes is initiated.
Journal Article
Feedback vertex set and longest induced path on AT-free graphs
TL;DR: In this paper, a polynomial time algorithm was proposed to compute a minimum (weight) feedback vertex set for AT-free graphs, and an O(nm 2 )-approximation algorithm for graphs of bounded asteroidal number.
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Complexity Framework For Forbidden Subgraphs
Matthew P. Johnson,Barnaby Martin,Jelle J. Oostveen,Sukanya Pandey,Daniël Paulusma,Siani Smith,Erik Jan van Leeuwen +6 more
TL;DR: In this paper , the authors proposed a meta-classification of subgraph-free graphs and showed that the problem of partitioning, covering and packing is solvable in polynomial time on subcubic graphs.
References
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Book
Parameterized Algorithms
Marek Cygan,Fedor V. Fomin,Lukasz Kowalik,Daniel Lokshtanov,Dániel Marx,Marcin Pilipczuk,Michał Pilipczuk,Saket Saurabh +7 more
TL;DR: This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area, providing a toolbox of algorithmic techniques.
Journal ArticleDOI
Graph minors. XIII: the disjoint paths problem
Neil Robertson,Paul Seymour +1 more
TL;DR: An algorithm, which for fixed k ≥ 0 has running time O (| V(G) | 3 ), to solve the following problem: given a graph G and k pairs of vertices of G, decide if there are k mutually vertex-disjoint paths of G joining the pairs.
Journal ArticleDOI
Hamilton Paths in Grid Graphs
TL;DR: This work gives necessary and sufficient conditions for the graph to have a Hamilton path between these two nodes, and provides a new, relatively simple, proof of the result that the Euclidean traveling salesman problem is NP-complete.
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Algorithms for Vertex Partitioning Problems on Partial k -Trees
TL;DR: A design methodology of practical solution algorithms for generally $\NP$-hard problems when restricted to partial k-trees (graphs with treewidth bounded by k) is presented, which accounts for dependency on the parameter k of the computational complexity of the resulting algorithms.
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Width Parameters Beyond Tree-width and their Applications
TL;DR: It is demonstrated how ‘width’ parameters of graphs and generalized structures, such as matroids or hypergraphs, can be used to improve the design of parameterized algorithms and the structural analysis in other applications on an abstract level.