Ervin Győri, Addisu Paulos, Nika Salia, Casey Tompkins, Oscar Zamora
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In 1979, Hakimi and Schmeichel considered the problem of maximizing the number of cycles of a given length in an -vertex planar graph. They precisely determined the maximum number of triangles and four-cycles and presented a conjecture for the maximum number of pentagons. In this work, we confirm their conjecture. Even more, we characterize the -vertex, planar graphs with the maximum number of pentagons.
期刊介绍：
The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences.
A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .
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