Superextensions and the depth of median graphs
Journal of Combinatorial Theory Series A
European Journal of Combinatorics - Special issue on discrete metric spaces
An Euler-type formula for median graphs
Discrete Mathematics
Concrete Mathematics: A Foundation for Computer Science
Concrete Mathematics: A Foundation for Computer Science
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
On the structure of the tight-span of a totally split-decomposable metric
European Journal of Combinatorics
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Median graphs are a natural generalisation of trees and hypercubes that are closely related to distributive lattices and graph retracts. In the past decade, they have become of increasing interest to the biological community, where, amongst other things, they are applied to the study of evolutionary relationships within populations. Two simple measures of complexity for a median graph are the number of vertices and the number of maximal induced subcubes. These numbers can be useful in biological applications, and they are also of purely mathematical interest. However, they can be hard to compute in general. Here we present some special families of median graphs where it is possible to find formulae and recursions for these numbers.