ISIPhyNC - Class: binary regular


Definition

A phylogenetic network is binary regular if it is binary and it is decontracted-regular. [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 #24 : If we contract each reticulation vertex of this network with its child, we obtain the Hasse diagram of {{1},{2},{3},{4},{1,2},{2,3},{3,4},{1,2,3},{2,3,4},{1,2,3,4}}.
network #2 : If we contract each reticulation vertex of this network with its child, we obtain the Hasse diagram of {{1},{2},{3},{4},{5},{1,2},{2,3},{1,2,3},{3,4},{1,2,3,4},{4,5},{1,2,3,4,5}}.
network #8 : If we contract each reticulation vertex of this network with its child, we obtain the Hasse diagram of {{1},{2},{3},{4},{5},{1,2},{2,3},{3,4},{2,3,4},{3,4,5},{1,2,3,4},{1,2,3,4,5}}.

Deduced from class inclusions: 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 #9 : c(b)={2,3} is contained in c(e)={2,3,4}, however there is no path from e to b.

Deduced from class inclusions: network #5 (deduced from the inclusion of this class in "binary distinct-cluster"), network #14 (deduced from the inclusion of this class in "binary FU-stable"), network #12 (deduced from the inclusion of this class in "binary compressed"), network #6 (deduced from the inclusion of this class in "binary distinct-cluster"), network #11 (deduced from the inclusion of this class in "binary distinct-cluster"), network #1 (deduced from the inclusion of this class in "binary distinct-cluster"), 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 #4 (deduced from the inclusion of this class in "binary distinct-cluster")

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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