ISIPhyNC - Class: binary nearly stable
Definition
A phylogenetic network is
binary nearly stable if it is
binary and it is
nearly stable. [
reference]
Bibliographic references on the Who is who in phylogenetic networks
Relationships with other phylogenetic network classes
Maximum subclasses
- binary tree-child [reference] (Noting that binary tree-child networks can be defined as binary phylogenetic networks whose vertices are all stable implies that binary tree-child networks are particular cases of nearly-stable networks.)
Minimum superclasses
Problems
Positive results proved for this class
Positive results deduced from superclasses
- Phylogenetic Network Isomorphism, positive result on binary: The phylogenetic network isomorphism problem can be solved in O(n^{4}) 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]
Negative results proved for this class
Negative results deduced from subclasses
No negative result could be deduced from subclasses.
Properties
Properties proved for this class
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 #1 : Vertices a, f and g are stable for leaf 1; vertex b is stable for leaf 2; vertex c is stable for leaf 3; vertices e and d are not stable but their respective parents f and g are.
network #3 : Reticulation vertices c and d are the only ones which are not stable but in both cases, both their parents are.
network #2 : The unique parents of the only vertices which are not stable, d and e, respectively b and a, are stable.
network #4 : All vertices except c and i (whose unique parent is in both cases stable) are stable.
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), network #7 (deduced from the inclusion of "binary normal" in this class), network #13 (deduced from the inclusion of "binary normal" in this class), network #22 (deduced from the inclusion of "binary normal" in this class), network #15 (deduced from the inclusion of "binary normal" in this class)
Not in this class
Proved directly:
network #17 : Vertex b is not stable and its parent d is not either.
network #21 : Vertex d is not stable and its parent b is not either.
network #19 : Vertex e is not stable and its parent d is not either.
network #8 : Vertex e is not stable and its parent d is not either.
Deduced from class inclusions: no network found outside this class using class inclusions
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).