%0 Generic %1 huber2020weakly %A Huber, Katharina T. %A Linz, Simone %A Moulton, Vincent %D 2020 %K 4330 graph phylogenic tree %T Weakly displaying trees in temporal tree-child network %U http://arxiv.org/abs/2004.02634 %X Recently there has been considerable interest in the problem of finding a phylogenetic network with a minimum number of reticulation vertices which displays a given set of phylogenetic trees, that is, a network with minimum hybrid number. Even so, for certain evolutionary scenarios insisting that a network displays the set of trees can be an overly restrictive assumption. In this paper, we consider the less restrictive notion of displaying called weakly displaying and, in particular, a special case of this which we call rigidly displaying. We characterize when two trees can be rigidly displayed by a temporal tree-child network in terms of fork-picking sequences, a concept that is closely related to that of cherry-picking sequences. We also show that, in case it exists, the rigid hybrid number for two phylogenetic trees is given by a minimum weight fork-picking sequence for the trees, and that the rigid hybrid number can be quite different from the related beaded- and temporal-hybrid numbers.

@misc{huber2020weakly, abstract = {Recently there has been considerable interest in the problem of finding a phylogenetic network with a minimum number of reticulation vertices which displays a given set of phylogenetic trees, that is, a network with minimum hybrid number. Even so, for certain evolutionary scenarios insisting that a network displays the set of trees can be an overly restrictive assumption. In this paper, we consider the less restrictive notion of displaying called weakly displaying and, in particular, a special case of this which we call rigidly displaying. We characterize when two trees can be rigidly displayed by a temporal tree-child network in terms of fork-picking sequences, a concept that is closely related to that of cherry-picking sequences. We also show that, in case it exists, the rigid hybrid number for two phylogenetic trees is given by a minimum weight fork-picking sequence for the trees, and that the rigid hybrid number can be quite different from the related beaded- and temporal-hybrid numbers.}, added-at = {2020-04-07T15:19:37.000+0200}, author = {Huber, Katharina T. and Linz, Simone and Moulton, Vincent}, biburl = {https://www.bibsonomy.org/bibtex/2ced7b88c23a5878f8c4c5a5716eb62ea/j.c.m.janssen}, description = {Weakly displaying trees in temporal tree-child network}, interhash = {a8f8bdb2c58726864c91468d03f3db3d}, intrahash = {ced7b88c23a5878f8c4c5a5716eb62ea}, keywords = {4330 graph phylogenic tree}, note = {cite arxiv:2004.02634}, timestamp = {2020-04-07T15:19:37.000+0200}, title = {Weakly displaying trees in temporal tree-child network}, url = {http://arxiv.org/abs/2004.02634}, year = 2020 }