Embedding a Forest in a Graph

For \math{p\ge 1}, we prove that every forest with \math{p} trees whose sizes are $a_1,…, a_p$ can be embedded in any graph containing at least $\sum_{i=1}^p (a_i + 1)$ vertices and having a minimum degree at least $\sum_{i=1}^p a_i$.

💡 Research Summary

The paper addresses the problem of embedding a collection of trees—collectively a forest—into a host graph under simple degree and size constraints. The authors prove a clean, optimal theorem: let (p\ge 1) and let (T_1,\dots ,T_p) be trees with vertex counts (a_1,\dots ,a_p). If a simple graph (G) satisfies
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