ISIPhyNC - Class: binary spread-1


Definition

A phylogenetic network is binary spread-1 if it is binary and it is spread-1. [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

Negative results proved for this class

Negative results deduced from subclasses


Properties

Properties proved for this class

Properties deduced from superclasses

Properties deduced from subclasses


Examples of networks

In this class

proved directly:
network #9 : Consider the order 1 2 3 4 of the leaves to obtain spread 1.

Deduced from class inclusions: network #5 (deduced from the inclusion of "binary unicyclic" in this class), network #12 (deduced from the inclusion of "binary leaf outerplanar" in this class), network #6 (deduced from the inclusion of "binary galled tree" in this class), network #11 (deduced from the inclusion of "binary leaf outerplanar" in this class), network #13 (deduced from the inclusion of "binary leaf outerplanar" in this class), network #1 (deduced from the inclusion of "binary leaf outerplanar" in this class), network #10 (deduced from the inclusion of "binary leaf outerplanar" in this class), network #2 (deduced from the inclusion of "binary leaf outerplanar" in this class), network #8 (deduced from the inclusion of "binary leaf outerplanar" in this class), network #4 (deduced from the inclusion of "binary leaf outerplanar" in this class), network #16 (deduced from the inclusion of "binary leaf outerplanar" in this class)

Not in this class

Proved directly:
network #7 : Suppose by contradiction that there exists an order where there is exactly one interval for each cluster. Clusters {2,3} of vertex c and {3,4} of vertex f force 3 to be between 2 and 4 in this order. So 1 cannot be between 2 and 3 nor between 4 and 3. Therefore, either cluster {1,2,3} of vertex a and {1,3,4} of vertex e have to appear as 2 intervals in this order (split respectively by 4 or by 2).
network #3 : Suppose there exists an order of the leaves which corresponds to spread 1. Vertices b, e, g, i are all above leaf 2 as well as above another leaf which is not below the other ones. So whatever two leaves, say 1 and 3, we choose to be around leaf 2 in the order, 4 and 5 will not be, so the leaves below g and h will not be an interval in this order.

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).

 

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