Level-2 networks from shortest and longest distances
Katharina T Huber (University of East Anglia)
Leo van Van Iersel (TU Delft - Discrete Mathematics and Optimization)
R. Janssen (TU Delft - Discrete Mathematics and Optimization)
Mark Jones (TU Delft - Discrete Mathematics and Optimization)
Vincent Moulton (University of East Anglia)
Yukihiro Murakami (TU Delft - Discrete Mathematics and Optimization)
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Abstract
Recently it was shown that a certain class of phylogenetic networks, called level-2 networks, cannot be reconstructed from their associated distance matrices. In this paper, we show that they can be reconstructed from their induced shortest and longest distance matrices. That is, if two level-2 networks induce the same shortest and longest distance matrices, then they must be isomorphic. We further show that level-2 networks are reconstructible from their shortest distance matrices if and only if they do not contain a subgraph from a family of graphs. A generator of a network is the graph obtained by deleting all pendant subtrees and suppressing degree-2 vertices. We also show that networks with a leaf on every generator side are reconstructible from their induced shortest distance matrix.
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