Mim-Width I. Induced path problems
- Authors
- Jaffke, Lars; Kwon, O jung; Telle, Jan Arne
- Issue Date
- May-2020
- Publisher
- ELSEVIER
- Keywords
- Graph classes; Graph width parameters; Hamiltonian cycle; Induced paths; Induced topological minors
- Citation
- DISCRETE APPLIED MATHEMATICS, v.278, pp.153 - 168
- Indexed
- SCIE
SCOPUS
- Journal Title
- DISCRETE APPLIED MATHEMATICS
- Volume
- 278
- Start Page
- 153
- End Page
- 168
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/189490
- DOI
- 10.1016/j.dam.2019.06.026
- ISSN
- 0166-218X
- Abstract
- We initialize a series of papers deepening the understanding of algorithmic properties of the width parameter maximum induced matching width (mim-width) of graphs. In this first volume we provide the first polynomial-time algorithms on graphs of bounded mim-width for problems that are not locally checkable. In particular, we give n(O(w))-time algorithms on graphs of mim-width at most w, when given a decomposition, for the following problems: LONGEST INDUCED PATH, INDUCED DISJOINT PATHS and H-INDUCED Topological Minor for fixed H. Our results imply that the following graph classes have polynomial-time algorithms for these three problems: INTERVAL and BI-INTERVAL graphs, CIRCULAR ARC, PERMUTATION and CIRCULAR PERMUTATION graphs, CONVEX graphs, k-TRAPEZOID, CIRCULAR k-TRAPEZOID, k-POLYGON, DILWORTH-k and Co-k-DEGENERATE graphs for fixed k. We contrast these positive results to the fact that problems about finding long non-induced paths remain hard on graphs of bounded mimwidth: We show 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.
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