Paths with restricted degrees of their vertices in planar graphs
Stanislav Jendrol′ · Czechoslovak Mathematical Journal · 1999
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 ≥ 3, k ≥ 4 there is a 2-connected planar graph such that every path on n vertices in it has a vertex of degree k .