Not All Saturated 3-Forests Are Tight

Details Not All Saturated 3-Forests Are Tight Not All Saturated 3-Forests Are Tight

2011-09-15

arxiv.org/abs/1109.3390v1

Mathematics

Combinatorics

Scientific paper

A basic statement in graph theory is that every inclusion-maximal forest is connected, i.e. a tree. Using a definiton for higher dimensional forests by Graham and Lovasz and the connectivity-related notion of tightness for hypergraphs introduced by Arocha, Bracho and Neumann-Lara in, we provide an example of a saturated, i.e. inclusion-maximal 3-forest that is not tight. This resolves an open problem posed by Strausz.

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