  Understanding the mutational history of tumor cells is a critical endeavor in
unraveling the mechanisms underlying cancer. Since the modeling of tumor cell
evolution employs labeled trees, researchers are motivated to develop different
methods to assess and compare mutation trees and other labeled trees. While the
Robinson-Foulds distance is a widely utilized metric for comparing phylogenetic
trees, its applicability to labeled trees reveals certain limitations. This
paper introduces the $k$-Robinson-Foulds dissimilarity measures, tailored to
address the challenges of labeled tree comparison. The Robinson-Foulds distance
is succinctly expressed as n-RF in the space of labeled trees with n nodes.
Like the Robinson-Foulds distance, the k-Robinson-Foulds is a pseudometric for
multiset-labeled trees and becomes a metric in the space of 1-labeled trees. By
setting k to a small value, the k-Robinson-Foulds dissimilarity can capture
analogous local regions in two labeled trees with different size or different
labels.
