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Edge-domatic numbers of cacti

Bohdan Zelinka (1991)

Mathematica Bohemica

The edge-domatic number of a graph is the maximum number of classes of a partition of its edge set into dominating sets. This number is studied for cacti, i.e. graphs in which each edge belongs to at most one circuit.

End-faithful spanning trees of countable graphs with prescribed sets of rays

Norbert Polat (2001)

Czechoslovak Mathematical Journal

We prove that a countable connected graph has an end-faithful spanning tree that contains a prescribed set of rays whenever this set is countable, and we show that this solution is, in a certain sense, the best possible. This improves a result of Hahn and Širáň Theorem 1.

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