Planar Graphs have Independence Ratio at least 3/13
نویسندگان
چکیده
The 4 Color Theorem (4CT) implies that every n-vertex planar graph has an independent set of size at least n4 ; this is best possible, as shown by the disjoint union of many copies of K4. In 1968, Erdős asked whether this bound on independence number could be proved more easily than the full 4CT. In 1976 Albertson showed (independently of the 4CT) that every n-vertex planar graph has an independent set of size at least 2n 9 . Until now, this remained the best bound independent of the 4CT. Our main result improves this bound to 3n 13 .
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عنوان ژورنال:
- Electr. J. Comb.
دوره 23 شماره
صفحات -
تاریخ انتشار 2016