Combinatorial Challenge II
نویسنده
چکیده
Please send further problems/challenges/conectures to Mike Steel Combinatorial Challenge I: Walking through trees Submitted by David Bryant An " NNI-‐walk " is a sequence T1, T2, …, Tk of unrooted binary phylogenetic trees where each consecutive pair of trees differ by a single NNI. i. [Question] What is the shortest NNI walk that passes through all binary trees on n leaves? ii. [Question] Suppose we are given a tree T. What is the shortest NNI walk that passes through all the trees that lie at most one SPR (subtree prune and regraft) move from T? Combinatorial Challenge II Submitted by Mike Steel Given two unrooted binary phylogenetic trees T, T', each with leaf set X of size n, an agreement set for T, T' is a subset Y of X for which T|Y= T'|Y. [Question] Is there a constant c, so that for any two trees T, T' have an agreement subtree of size c ! log n ? Computational Complexity Challenge: Perfect taxon sampling Submitted by Mike Steel A collection S of subsets of X is said to be phylogenetically decisive 1 if for every binary phylogenetic X-‐tree T, the collection T|Y: Y \in S defines T (i.e. T is the only tree that displays these trees). [Question] What is the computational complexity of determining whether S is phylogenetically decisive? This may be related to the 'No-‐rainbow-‐colouring' problem of Manuel Bodirsky, whose complexity appears still open.
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