Abstract
For every graph H, there exists a polynomial-time algorithm deciding if a planar input graph G can be contracted to H. However, the degree of the polynomial depends on the size of H. We identify a class of graphs C such that for every fixed H C, there exists a linear-time algorithm deciding whether a given planar graph G can be contracted to H. The class C is the closure of planar triangulated graphs under taking of contractions. In fact, we prove that a graph H C if and only if there exists a constant cH such that if the treewidth of a graph is at least cH, it contains H as a contraction. We also provide a characterization of C in terms of minimal forbidden contractions.
Original language | English (US) |
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Pages (from-to) | 299-306 |
Number of pages | 8 |
Journal | Journal of Discrete Algorithms |
Volume | 9 |
Issue number | 3 |
DOIs | |
State | Published - Sep 2011 |
Keywords
- Contraction
- Dual graph
- Fixed parameter tractable
- Planar graph
- Topological minor
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics