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).
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This research was conducted while the author served as a Clay Mathematics Institute Research Fellow.
Supported by ONR grant N00014-01-1-0608, and NSF grant DMS-0070912.
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Chudnovsky, M., Seymour, P. The three-in-a-tree problem. Combinatorica 30, 387–417 (2010). https://doi.org/10.1007/s00493-010-2334-4
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DOI: https://doi.org/10.1007/s00493-010-2334-4