Sub-exponentially many 3-colorings of triangle-free planar graphs

Details Sub-exponentially many 3-colorings of triangle-free planar graphs Sub-exponentially many 3-colorings of triangle-free planar graphs

2010-07-08

arxiv.org/abs/1007.1430v2

Mathematics

Combinatorics

10 pages. Simplified proof. Added a coauthor

Scientific paper

Thomassen conjectured that every triangle-free planar graph on n vertices has
exponentially many 3-colorings, and proved that it has at least
2^[n^(1/12)/20000] distinct 3-colorings. We show that it has at least
2^sqrt(n/362) distinct 3-colorings.

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