Polytomies of degree 4 or 5 cannot be handled using the double anchored approach because once two clusters are chosen as anchors, only two or three clusters remain which cannot be resolved as unrooted trees. For these small polytomies, we always use all-pairs distance matrices; thus, we choose all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${4 \choose 2}$\end{document}42 or \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${5 \choose 2}$\end{document}52 possible pairs of clusters around the polytomy. We need O(n) anchors in this scenario as well (Additional file 1: Lemma S2).