Abstract
Modifying a given graph to obtain another graph is a well-studied problem with applications in many fields. Given two input graphs G and H, the Contractibility problem is to decide whether H can be obtained from G by a sequence of edge contractions. This problem is known to be NP-complete already when both input graphs are trees of bounded diameter. We prove that Contractibility can be solved in polynomial time when G is a trivially perfect graph and H is a threshold graph, thereby giving the first classes of graphs of unbounded treewidth and unbounded degree on which the problem can be solved in polynomial time. We show that this polynomial-time result is in a sense tight, by proving that Contractibility is NP-complete when G and H are both trivially perfect graphs, and when G is a split graph and H is a threshold graph. If the graph H is fixed and only G is given as input, then the problem is called H-Contractibility. This problem is known to be NP-complete on general graphs already when H is a path on four vertices. We show that, for any fixed graph H, the H-Contractibility problem can be solved in polynomial time if the input graph G is a split graph.
Original language | English |
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Title of host publication | Theory and Applications of Models of Computation - 8th Annual Conference, TAMC 2011, Tokyo, Japan, May 23-25, 2011. Proceedings |
Editors | Mitsunori Ogihara, Jun Tarui |
Publisher | Springer |
Pages | 528-539 |
Number of pages | 12 |
ISBN (Electronic) | 978-3-642-20877-5 |
ISBN (Print) | 978-3-642-20876-8 |
DOIs | |
Publication status | Published - 2011 |
Externally published | Yes |
Event | 8th Annual Conference on Theory and Applications of Models of Computation, TAMC 2011 - Tokyo, Japan Duration: 23 May 2011 → 25 May 2011 Conference number: 8 |
Publication series
Name | Lecture Notes in Computer Science |
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Publisher | Springer |
Volume | 6648 |
Conference
Conference | 8th Annual Conference on Theory and Applications of Models of Computation, TAMC 2011 |
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Abbreviated title | TAMC 2011 |
Country/Territory | Japan |
City | Tokyo |
Period | 23/05/11 → 25/05/11 |