Connecting Face Hitting Sets in Planar Graphs

Schweitzer, Pascal; Schweitzer, Patrick

doi:10.1016/j.ipl.2010.10.008

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Connecting Face Hitting Sets in Planar Graphs

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Schweitzer, Pascal
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Citation

Schweitzer, P., & Schweitzer, P. (2010). Connecting Face Hitting Sets in Planar Graphs. Information Processing Letters, 111(1), 11-15. doi:10.1016/j.ipl.2010.10.008.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-162F-4

Abstract

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−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 11n−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.