Szervusztok! A félév utolsó péntekén
Authors: \'Eva Czabarka, L\'aszl\'o Sz\'ekely, Zolt\'an Toroczkai, Shanise Walker
Abstract: The problem that we discuss is the following: Can we realize a given degree sequence, such that we also satisfy two further restrictions simultaneously: (i) some pairs are forbidden to use as an edge, and (ii) the vertex set is partitioned into classes, and the number of edges in the realization should give prescribed number of edges between (and within) partition classes. This problem is relevant for network science. The talk focuses on the bipartite version of this problem.
Abstract. A tanglegram consists of two rooted binary plane trees with the same number of leaves and a perfect matching between the two leaf sets. Tanglegrams are drawn with the leaves on two parallel lines, the trees on either side of the strip created by these lines, and the perfect matching inside the strip. If this can be done without any edges crossing, a tanglegram is called planar. We show that every non-planar tanglegram contains one of two non-planar 4-leaf tanglegrams as induced subtanglegram, which parallels Kuratowski’s Theorem.
Joint work with Laszlo A. Szekely and Stephan Wagner
Minden érdeklődőt szeretettel várunk, Péter