There Are Spanning Spiders in Dense Graphs (and We Know How to Find Them)

@inproceedings{Gargano2003ThereAS,
  title={There Are Spanning Spiders in Dense Graphs (and We Know How to Find Them)},
  author={Luisa Gargano and Mikael Hammar},
  booktitle={ICALP},
  year={2003}
}
A spanning spider for a graph G is a spanning tree T of G with at most one vertex having degree three or more in T. In this paper we give density criteria for the existence of spanning spiders in graphs. We constructively prove the following result: Given a graph G with n vertices, if the degree sum of any independent triple of vertices is at least n - 1, then there exists a spanning spider in G. We also study the case of bipartite graphs and give density conditions for the existence of a… CONTINUE READING

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