# Article

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Summary:
In this paper it is proved that every \$3\$-connected planar graph contains a path on \$3\$ vertices each of which is of degree at most \$15\$ and a path on \$4\$ vertices each of which has degree at most \$23\$. Analogous results are stated for \$3\$-connected planar graphs of minimum degree \$4\$ and \$5\$. Moreover, for every pair of integers \$n\ge 3\$, \$ k\ge 4\$ there is a \$2\$-connected planar graph such that every path on \$n\$ vertices in it has a vertex of degree \$k\$.
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