LOCAL QUARTET SPLITS OF A BINARY-TREE INFER ALL QUARTET SPLITS VIA ONE DYADIC INFERENCE RULE

A significant problem in phylogeny is to reconstruct a semilabelled bi nary tree from few valid quartet splits of it. It is well-known that e very semilabelled binary tree is determined by its set of all valid qu artet splits. Here Re strengthen this result by showing that its local (i.e. small diameter) quartet splits infer tv a dyadic inference rule all valid quartet splits. and hence determine the tree. The results o f the paper also present a polynomial time algorithm to recover the tr ee.