Recent Progress in Phylogenetic Combinatorics
نویسنده
چکیده
of D is an R-tree. (ii) There exists a tree (V, E ) whose vertex set V contains X, and an edge weighting C : E -i R that assigns a positive length C(e) to each edge e in E , such that D is the restriction of X to the shortest-path metric induced on V. (iii) There exists a map w : S(X) -i R>o from the set S(X) of all bi-partitions or splits of X into the set R ~ o of non-negative real numbers such that, given any two splits S = { A , B } and S’ = {A’, B’} in S ( X ) with w(S), w(S’) # 0, at least one of the four intersections A n A‘, B n A’, A n B’, and B n B’ is empty and D(x, y) = CSES(X:zcrV) w(S) holds where S ( X : z-y) denotes the set of splits S = { A , B } E S(X) that separate z and y. (iv) D ( z , y) + D(u, v) 5 max ( D ( z , u) + D(y, v), D ( z , v) + D(y, u)) holds for all X,Y,U,V E X
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