Extremal Problems For Transversals In Graphs With Bounded Degree

@article{Szab2006ExtremalPF,
  title={Extremal Problems For Transversals In Graphs With Bounded Degree},
  author={Tibor Szab{\'o} and G{\'a}bor Tardos},
  journal={Combinatorica},
  year={2006},
  volume={26},
  pages={333-351}
}
We introduce and discuss generalizations of the problem of independent transversals. Given a graph property R, we investigate whether any graph of maximum degree at most d with a vertex partition into classes of size at least p admits a transversal having property R. In this paper we study this problem for the following properties R: “acyclic”, “H-free”, and “having connected components of order at most r”. We strengthen a result of [13]. We prove that if the vertex set of a d-regular graph is… CONTINUE READING

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