Analogies between the Crossing Number and the Tangle Crossing Number

摘要

Tanglegrams are special graphs that consist of a pair of rooted binary trees with the same number of leaves, and a perfect matching between the two leaf-sets. These objects are of use in phylogenetics and are represented with straight-line drawings where the leaves of the two plane binary trees are on two parallel lines and only the matching edges can cross. The tangle crossing number of a tanglegram is the minimum number of crossings over all such drawings and is related to biologically relevant quantities, such as the number of times a parasite switched hosts.