According to the classic Chv{\'{a}}tal's Lemma from 1977, a graph of minimum degree $\delta(G)$ contains every tree on $\delta(G)+1$ vertices. Our main result is the following algorithmic "extension" of Chv\'{a}tal's Lemma: For any $n$-vertex graph $G$, integer $k$, and a tree $T$ on at most $\delta(G)+k$ vertices, deciding whether $G$ contains a subgraph isomorphic to $T$, can be done in time $f(k)\cdot n^{\mathcal{O}(1)}$ for some function $f$ of $k$ only. The proof of our main result is based on an interplay between extremal graph theory and parameterized algorithms.

翻译：根据1977年Chvátal引理的经典结论，最小度为δ(G)的图包含所有顶点数不超过δ(G)+1的树。我们的主要结果是Chvátal引理的如下算法“扩展”：对于任意n顶点图G、整数k以及顶点数不超过δ(G)+k的树T，判定G是否包含与T同构的子图可在时间f(k)·n^O(1)内完成，其中f是仅依赖于k的函数。该主要结果的证明基于极值图论与参数化算法之间的相互关联。