Connecting face hitting sets in planar graphs

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Connecting face hitting sets in planar graphs
We show that any face hitting set of size n of a connected planar graph with a minimum degree of at least 3 is contained in a connected subgraph of size 5n āˆ’ 6. Furthermore we show that this bound is tight by providing a lower bound in the form of a family of graphs. This improves the previously known upper and lower bound of 11nāˆ’18 and 3n respectively by Grigoriev and Sitters. Our proof is valid for simple graphs with loops and generalizes to graphs embedded in surfaces of arbitrary genus.
Pascal Schweitzer, Patrick Schweitzer
Added 28 Jan 2011
Updated 28 Jan 2011
Type Journal
Year 2010
Where IPL
Authors Pascal Schweitzer, Patrick Schweitzer
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