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Fig. 1 | Algorithms for Molecular Biology

Fig. 1

From: Using Robinson-Foulds supertrees in divide-and-conquer phylogeny estimation

Fig. 1

\(T_1\) and \(T_2\) (depicted in (a) and (b), respectively) have an overlapping leaf set \(X = \{l_1,l_2,\dots ,l_7\}\). Each of \(a_1,\dots , a_6\) and \(b_1,\dots , b_6\) can represent a multi-leaf extra subtree. For \(e \in T_1|_X\) as shown, P(e) is the path from \(v_1\) to \(v_4\), so \(w(e) = 3\). Using indices to represent the shared leaves, let \(\pi = [12 | 34567]\); then \(e_1(\pi ) = e\) and \(e_2(\pi ) = e'\). \(\mathcal {TR}(e) = \{a_1,a_2\}\), \(\mathcal {TR}(e') = \{b_2\}\), so \(\mathcal {TR}^*(\pi ) = \{a_1,a_2,b_2\}\). Let \(A = \{1,2,3\}\), \(B = \{4,5,6,7\}\). Ignoring the trivial bipartitions, we have \(\mathcal {BP}(A) = \{[12|34567] \}\) and \(\mathcal {BP}(B) = \{[1234|567],[12345|67],[12346|57]\}\). \(\mathcal {TRS}(A) = \{a_1,a_2,b_1,b_2\}\) and \(\mathcal {TRS}(B) = \{ a_6,b_4,b_5,b_6\}\)

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