ISIPhyNC - Class: binary level-2
Definition
A phylogenetic network is binary level-2 if it is binary and it is level-2. [reference]Bibliographic references on the Who is who in phylogenetic networks
Relationships with other phylogenetic network classes
Maximum subclasses
- binary galled tree (A binary galled tree is actually a binary level-1 network.)
Minimum superclasses
- binary 2-reticulated [reference]
- binary level-3
- binary spread-2 [reference] (The inclusion of level-2 inside spread-3 was given in this reference)
- binary tree-based [reference]
Problems
Positive results proved for this class
- Cluster Containment: Solvable in O(n) time [reference] (Observation 1)
- Tree Containment: Solvable in O(n) time [reference] (Observation 1)
Positive results deduced from superclasses
- Cluster Containment, positive result on binary level-3: Solvable in O(n) time [reference] (Observation 1)
- Cluster Containment, positive result on binary level-k: Solvable in O(2k.n) time [reference] (Observation 1)
- Phylogenetic Network Isomorphism, positive result on binary: The phylogenetic network isomorphism problem can be solved in O(n4) time on binary networks. Simulations show that the algorithm is practical, with instances of 500 vertices solved in less than one tenth of a second. [reference]
- Tree Containment, positive result on binary level-3: Solvable in O(n) time [reference] (Observation 1)
- Tree Containment, positive result on binary level-k: Solvable in O(2k.n) time [reference] (Observation 1)
Negative results proved for this class
-
No negative result found
Negative results deduced from subclasses
-
No negative result could be deduced from subclasses.
Properties
Properties proved for this class
-
No property found
Properties deduced from superclasses
-
No property could be deduced from superclasses.
Properties deduced from subclasses
-
No property could be deduced from subclasses.
Examples of networks
In this class
proved directly:
network #12 :
network #14 : The network only has 2 reticulation vertices.
network #17 : The network only has 2 reticulation vertices.
network #7 :
network #9 :
network #13 :
network #4 :
Deduced from class inclusions: network #5 (deduced from the inclusion of "binary unicyclic" in this class), network #6 (deduced from the inclusion of "binary galled tree" in this class)
Not in this class
Proved directly:
network #11 :
network #1 :
network #3 : c, d and h are three reticulation vertices in the same blob.
network #2 :
network #8 :
Deduced from class inclusions: network #7 (deduced from the inclusion of this class in "binary 2-reticulated"), network #10 (deduced from the inclusion of this class in "binary tree-based"), network #3 (deduced from the inclusion of this class in "binary tree-based"), network #16 (deduced from the inclusion of this class in "binary level-3"), network #18 (deduced from the inclusion of this class in "binary level-3"), network #23 (deduced from the inclusion of this class in "binary level-3"), network #15 (deduced from the inclusion of this class in "binary level-3")
About this website
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.
How to cite
P. Gambette, M. Morgado, N. Tavassoli & M. Weller (2018) ISIPhyNC, an Information System on Inclusions of Phylogenetic Network Classes, manuscript in preparation.
Database content
73 classes of phylogenetic networks including 35 classes of binary phylogenetic networks (defined in a total of 20 bibliographic references), 51 inclusion relationships proved directly between classes (including some found in a total of 9 bibliographic references), 24 networks (68 memberships to a class, 56 non-memberships to a class), 3 problems considered, 3 properties considered, 37 theorems proved directly (including some found in a total of 17 bibliographic references) including 26 positive results (which can be extended to subclasses) and 11 negative results (which can be extended to superclasses).
