# Robust Connectivity of Graphs on Surfaces

```@article{Bradshaw2022RobustCO,
title={Robust Connectivity of Graphs on Surfaces},
journal={ArXiv},
year={2022},
volume={abs/2104.12030}
}```
• Published 24 April 2021
• Mathematics
• ArXiv
Let Λ(T ) denote the set of leaves in a tree T . One natural problem is to look for a spanning tree T of a given graph G such that Λ(T ) is as large as possible. This problem is called maximum leaf number, and it is a well-known NP-hard problem. Equivalently, the same problem can be formulated as the minimum connected dominating set problem, where the task is to find a smallest subset of vertices D ⊆ V (G) such that every vertex of G is in the closed neighborhood of D. Throughout recent decades…

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