ISIPhyNC - Class: binary 3-reticulated

Definition

Relationships with other phylogenetic network classes

Maximum subclasses

• binary 2-reticulated
• binary level-3 [reference]

Minimum superclasses

• binary k-reticulated

Problems

Positive results proved for this class

No positive result found

Positive results deduced from superclasses

• 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]

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

• Unbounded number of vertices, property of binary nested: By subdividing the arc below the root of a blob on a side which contains a leaf, subdividing the arc above the reticulation arc of the same blob on the same s, and adding an arc from the vertex created by the first subdivision to the vertex created by the second subdivision, we increase the number of arcs and vertices of the network without increasing the number of leaves, and the network remains nested.

Examples of networks

In this class

proved directly:
no network found in this class with a direct proof

Deduced from class inclusions: network #20 (deduced from the inclusion of "binary nested" in this class), network #5 (deduced from the inclusion of "binary unicyclic" in this class), network #12 (deduced from the inclusion of "binary level-2" in this class), network #14 (deduced from the inclusion of "binary level-2" in this class), network #17 (deduced from the inclusion of "binary level-2" in this class), network #6 (deduced from the inclusion of "binary galled tree" in this class), network #11 (deduced from the inclusion of "binary level-3" in this class), network #7 (deduced from the inclusion of "binary level-2" in this class), network #9 (deduced from the inclusion of "binary level-2" in this class), network #13 (deduced from the inclusion of "binary level-2" in this class), network #1 (deduced from the inclusion of "binary level-3" in this class), network #10 (deduced from the inclusion of "binary level-3" in this class), network #19 (deduced from the inclusion of "binary 3-nested" in this class), network #3 (deduced from the inclusion of "binary level-3" in this class), network #2 (deduced from the inclusion of "binary level-3" in this class), network #8 (deduced from the inclusion of "binary level-3" in this class), network #4 (deduced from the inclusion of "binary level-2" in this class), network #16 (deduced from the inclusion of "binary 2-nested" in this class)

Not in this class

Proved directly:
no network found outside this class with a direct proof

Deduced from class inclusions: no network found outside this class using class inclusions