Simon Máté: Connectivity-Keeping Trees in Connected and k-Connected Graphs

Let T be any tree on d vertices. In this talk we prove that every connected graph with minimum degree d contains a subtree T' isomorphic to T whose removal leaves the graph still connected. We then turn to the k-connected case. Here we also discuss degree conditions that guarantee the existence of a copy of T whose deletion preserves k-connectivity.

Main papers:
https://www.sciencedirect.com/science/article/pii/S0012365X09001630
https://onlinelibrary.wiley.com/doi/abs/10.1002/jgt.20585

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