Mathematics – Combinatorics
Scientific paper
2010-04-05
Mathematics
Combinatorics
14 pages, 16 figures
Scientific paper
Two cycles are {\em adjacent} if they have an edge in common. Suppose that
$G$ is a planar graph, for any two adjacent cycles $C_{1}$ and $C_{2}$, we have
$|C_{1}| + |C_{2}| \geq 11$, in particular, when $|C_{1}| = 5$, $|C_{2}| \geq
7$. We show that the graph $G$ is 3-colorable.
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