# ISIPhyNC - Class: binary 3-nested

## Definition

A phylogenetic network is

*binary 3-nested* if it is

binary and it is

3-nested. [

reference]

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

## Relationships with other phylogenetic network classes

### Maximum subclasses

### 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 #19 :

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 #10 (deduced from the inclusion of "binary 2-nested" in this class), network #3 (deduced from the inclusion of "binary 2-nested" in this class), network #16 (deduced from the inclusion of "binary 2-nested" in this class)

### Not in this class

Proved directly:

network #20 : There are 4 reticulation cycles with distinct reticulation vertex containing vertex *d*: with reticulation vertex *e*, *f*, *g* and *h*.

Deduced from class inclusions: network #12 (deduced from the inclusion of this class in "binary nested"), network #14 (deduced from the inclusion of this class in "binary 1-reticulated"), network #11 (deduced from the inclusion of this class in "binary nested"), network #7 (deduced from the inclusion of this class in "binary nested"), network #9 (deduced from the inclusion of this class in "binary 1-reticulated"), network #1 (deduced from the inclusion of this class in "binary nested"), network #2 (deduced from the inclusion of this class in "binary nested"), network #8 (deduced from the inclusion of this class in "binary 1-reticulated"), network #4 (deduced from the inclusion of this class in "binary nested")

## 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).