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arXiv · 2310.09678

Tree Containment Above Minimum Degree is FPT

Fedor V. Fomin·Petr A. Golovach·Danil Sagunov·Kirill Simonov
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Abstract

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.

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Fedor V. Fomin, Petr A. Golovach, Danil Sagunov, Kirill Simonov. 2023-10-14. Tree Containment Above Minimum Degree is FPT. https://arxiv.org/abs/2310.09678

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