Abstract
The gravity of a graph H in a given family of graphs H is the greatest integer n with the property that for every integer m, there exists a supergraph G ∈ H of H such that each subgraph of G, which is isomorphic to H, contains at least n vertices of degree ⩾ m in G. Madaras and Škrekovski introduced this concept and showed that the gravity of the path P k on k ⩾ 2 vertices in the family of planar graphs of minimum degree 2 is k - 2 for each k ≠ 5 , 7 , 8 , 9 . They conjectured that for each of the four excluded cases the gravity is k - 3 . In this paper we show that this holds.
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