Combinatorica

, Volume 30, Issue 4, pp 387–417 | Cite as

The three-in-a-tree problem

Article

Abstract

We show that there is a polynomial time algorithm that, given three vertices of a graph, tests whether there is an induced subgraph that is a tree, containing the three vertices. (Indeed, there is an explicit construction of the cases when there is no such tree.) As a consequence, we show that there is a polynomial time algorithm to test whether a graph contains a “theta” as an induced subgraph (this was an open question of interest) and an alternative way to test whether a graph contains a “pyramid” (a fundamental step in checking whether a graph is perfect).

Mathematics Subject Classification (2000)

05C75 

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References

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Copyright information

© János Bolyai Mathematical Society and Springer Verlag 2010

Authors and Affiliations

  1. 1.Department of Industrial Engineering and Operations ResearchColumbia UniversityNew YorkUSA
  2. 2.Dept of MathematicsPrinceton UniversityPrincetonUSA

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