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A new 2-parameter family of central structures in trees, called central forests, is introduced. Miniekas $m$-center problem and McMorriss and Reids central-$k$-tree can be seen as special cases of central forests in trees. A central forest is defined as a forest $F$ of $m$ subtrees of a tree $T$, where each subtree has $k$ nodes, which minimizes the maximum distance between nodes not in $F$ and those in $F$. An $O(n(m+k))$ algorithm to construct such a central forest in trees is presented, where $n$ is the number of nodes in the tree. The algorithm either returns with a central forest, or with the largest $k$ for which a central forest of $m$ subtrees is possible. Some of the elementary properties of central forests are also studied.
While the game chromatic number of a forest is known to be at most 4, no simple criteria are known for determining the game chromatic number of a forest. We first state necessary and sufficient conditions for forests with game chromatic number 2 and
We characterize and study variable importance (VIMP) and pairwise variable associations in binary regression trees. A key component involves the node mean squared error for a quantity we refer to as a maximal subtree. The theory naturally extends fro
The study of patterns in permutations associated with forests of binary shrubs was initiated by D. Bevan et al.. In this paper, we study five different types of rise statistics that can be associated with such permutations and find the generating fun
Let $G$ be a graph on $n$ vertices. For $iin {0,1}$ and a connected graph $G$, a spanning forest $F$ of $G$ is called an $i$-perfect forest if every tree in $F$ is an induced subgraph of $G$ and exactly $i$ vertices of $F$ have even degree (including
Since their inception in the 1980s, regression trees have been one of the more widely used non-parametric prediction methods. Tree-structured methods yield a histogram reconstruction of the regression surface, where the bins correspond to terminal no