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arXiv · 2101.11777

Mader's conjecture for graphs with small connectivity

Yanmei Hong·Qinghai Liu
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Abstract

Mader conjectured that for any tree $T$ of order $m$, every $k$-connected graph $G$ with minimum degree at least $\lfloor\frac{3k}{2}\rfloor +m-1$ contains a subtree $T'\cong T$ such that $G-V(T')$ is $k$-connected. In this paper, we give a characterization for a subgraph to contain an embedding of a specified tree avoiding some vertex. As a corollary, we confirm Mader's conjecture for $k\leq3$.

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Yanmei Hong, Qinghai Liu. 2021-01-28. Mader's conjecture for graphs with small connectivity. https://arxiv.org/abs/2101.11777

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