Your code is probably falling into an infinite loop in some edge cases, make sure that your code can handle ties between competitors

class Tree {
  constructor(cats) { this.cats = cats; }
  getPathsOf(cat) { /* body with this.cats instead of cats .. */ return toReturn; }
}

or simply

Object.prototype.getPathsOf = function(cat) { /* body with this instead of cats .. */ return toReturn; };

In the latter case, please look into Object.defineProperty because of enumerability.

Does this answer your question?