proved directly:
network #12 : Removing the reticulation arcs (c,a) and (d,b) provides a tree this network is based on.
network #1 : Removing the reticulation arcs (f,a), (e,b) and (d,c) provides a tree this network is based on.
Deduced from class inclusions: network #5 (deduced from the inclusion of "binary unicyclic" in this class), network #14 (deduced from the inclusion of "binary compressed" in this class), network #12 (deduced from the inclusion of "binary tree-sibling" 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 FU-stable" in this class), network #7 (deduced from the inclusion of "binary galled network" in this class), network #9 (deduced from the inclusion of "binary distinct-cluster" 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 #1 (deduced from the inclusion of "binary galled network" in this class), network #21 (deduced from the inclusion of "binary galled network" in this class), network #24 (deduced from the inclusion of "binary regular" in this class), network #2 (deduced from the inclusion of "binary galled network" in this class), network #8 (deduced from the inclusion of "binary nearly tree-child" in this class), network #18 (deduced from the inclusion of "binary galled network" in this class), network #4 (deduced from the inclusion of "binary FU-stable" in this class), network #15 (deduced from the inclusion of "binary normal" in this class)
Proved directly:
network #10 :
network #3 : Suppose N is tree-based, and consider the tree T it is based on. If reticulation arc (c,d) is chosen in T, there would remain no leaf below h in T. A symmetric argument works for arc (h,d) and c, which leads to a contradiction.
Deduced from class inclusions: no network found outside this class using class inclusions
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.