ISIPhyNC - Class: binary leaf outerplanar

Definition

Relationships with other phylogenetic network classes

Maximum subclasses

• binary galled tree (It is possible to draw a binary galled tree with no leaf inside the galls in order to obtain an outerplanar realization.)

Minimum superclasses

• binary spread-1 [reference]

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

No property could be deduced from subclasses.

Examples of networks

In this class

proved directly:
network #12 :
network #12 : The network can be drawn in a planar way such that leaves 1 and 2 are in the outer face r-a-b-d-c-r.
network #11 :
network #13 :
network #1 :
network #10 :
network #2 :
network #8 :
network #4 :
network #16 : The network can be drawn in a planar way such that leaves 1, 2, 3 and 4 are in the outer face r-a-b-c-d-e-f-g-h-i-j-r.

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)

Not in this class

Proved directly:
network #9 :

Deduced from class inclusions: network #7 (deduced from the inclusion of this class in "binary spread-1"), network #3 (deduced from the inclusion of this class in "binary spread-1")