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Daniel Cranston, Vertex Partitions into an Independent Set and a Forest with Each Component Small
Daniel Cranston, Vertex Partitions into an Independent Set and a Forest with Each Component Small
For each integer $k\ge 2$, we determine a sharp bound on $\operatorname{mad}(G)$ such that $V(G)$ can be partitioned into sets $I$ and $F_k$, where $I$ is an independent set and $G$ is a forest in which each component has at most k vertices. For each $k$ we construct an infinite family of examples showing our result is best …