The 7-cycle C7C7 is light in the family of planar graphs with minimum degree 5

A connected graph H   is said to be light in the family of graphs HH if there exists a positive integer k   such that each graph G∈HG∈H that contains an isomorphic copy of H contains a subgraph K isomorphic to H   that satisfies the inequality ∑v∈V(K)degG(v)⩽k. It is known that an r  -cycle CrCr is light in the family of planar graphs with minimum degree 5 if 3⩽r⩽63⩽r⩽6, and not light for r⩾11r⩾11. We prove that C7C7 is also light in this family.