Connecting face hitting sets in planar graphs
نویسندگان
چکیده
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.
منابع مشابه
A note on 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−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 [8]. Our proof is valid for simple graphs ...
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عنوان ژورنال:
- Inf. Process. Lett.
دوره 111 شماره
صفحات -
تاریخ انتشار 2010