At-Most-k-Furcation

A k-furcating internal node for k>1 is an internal node that diverges into exactly k branches. For k>2, an at-most-k-furcating internal node, as studied by Maranca & Rosenberg (bioRxiv https://doi.org/10.1101/2023.04.19.537492, 2023) is an internal node for which the number of emanating branches is at least 2 and is bounded above by k — but need not equal k. At-most-k-furcating trees are trees for which all internal nodes diverge into at least 2 and at most k branches.For k>2, for an at-most-k-furcating internal node that has fewer than k emanating branches, it is convenient to regard the node has having “empty” positions that do not contain branches. Baseball fans can spot the phenomenon up close in the far left field stands at Sunken Diamond, where this at-most-5-furcating node has only 4 descending branches. As the saying goes, you can’t beat fun at the old ball park.