Title of article :
The Minimum Number of 4-Cycles in a Maximal Planar Graph with Small Number of Vertices
Author/Authors :
Győri ، Ervin Department of Mathematics - Alfréd Rényi Institute of Mathematics - Hungarian Academy of Sciences , Paulos ، Addisu Department of Mathematics - School of Mathematics and Statistics - Central European University , Zamora ، Oscar Department of Mathematics - School of Mathematics and Statistics - Central European University
Abstract :
Hakimi and Schmeichel determined a sharp lower bound for the number of cycles of length 4 in a maximal planar graph with n vertices, n ≥ 5. It has been shown that the bound is sharp for n = 5, 12 and n ≥ 14 vertices. However, the authors only conjectured the minimum number of cycles of length 4 for maximal planar graphs with the remaining small vertex numbers. In this note, we confirm their conjecture.
Keywords :
Planar graphs , Maximal planar graphs , 4 , cycle ,
Journal title :
Bulletin of the Iranian Mathematical Society
Journal title :
Bulletin of the Iranian Mathematical Society
