Does the input network contain the input tree on the same set of leaves? [reference]

Bibliographic references on the *Who is who in phylogenetic networks*

**Input:** A phylogenetic network *N* and a tree *T* on the same set *X* of taxa.

**Output:** YES if *N* contains *T*, NO otherwise.

- binary level-2: Solvable in O(
*n*) time [reference] (Observation 1) - binary level-3: Solvable in O(
*n*) time [reference] (Observation 1) - binary level-k: Solvable in O(2
^{k}.*n*) time [reference] (Observation 1) - binary nearly stable: Solvable in O(
*n*^{2}) time [reference] - binary nearly stable: Solvable in O(
*n*log*n*) time [reference] - binary nearly stable: Solvable in O(
*n*) time [reference] - binary normal: Solvable in polynomial time [reference] (Theorem 2)
- binary reticulation-visible: Solvable in O(
*n*^{3}) time [reference] - binary reticulation-visible: Solvable in O(
*n*) time [reference] - binary reticulation-visible: Solvable in O(
*n*) time [reference] - binary tree-child: Solvable in polynomial time [reference] (Theorem 1)

- binary: NP-hard, reduction from Node-disjoint Paths [reference] (Theorem 3.1)
- binary regular: NP-hard, reduction from Tree Containment on binary networks. [reference] (Theorem 3)
- binary spread-1: NP-complete, by a reduction from the general TreeContainment problem [reference]
- binary time-consistent: NP-hard, reduction from Tree Containment on binary networks. [reference] (Theorem 3)
- binary tree-sibling: NP-hard, reduction from Tree Containment on binary networks. [reference] (Theorem 3)

In the inclusion diagram below, the names of classes with positive results on this problem are colored green and the name of the classes with negative results are colored red. Classes with both positive and negative results are colored yellow.

This website was programmed and is maintained by Philippe Gambette. It was started during the internship of Maxime Morgado at LIGM, in June-July 2015, and also contains contributions made from Narges Tavassoli from November 2016 to January 2017.

Please contact Philippe Gambette if you have any suggestions about this website, especially about problems, properties, results or subclasses to add.