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The maximum number of induced C 5 's in a planar graph
Author(s) -
Ghosh Debarun,
Győri Ervin,
Janzer Oliver,
Paulos Addisu,
Salia Nika,
Zamora Oscar
Publication year - 2022
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.22745
Subject(s) - mathematics , combinatorics , planar graph , wheel graph , graph , vertex (graph theory) , outerplanar graph , butterfly graph , discrete mathematics , planar , crossing number (knot theory) , graph power , line graph , voltage graph , computer science , computer graphics (images) , intersection (aeronautics) , engineering , aerospace engineering
Finding the maximum number of induced cycles of length k in a graph on n vertices has been one of the most intriguing open problems of Extremal Graph Theory. Recently Balogh, Hu, Lidický and Pfender answered the question in the case k = 5 . In this paper we determine precisely, for all sufficiently large n , the maximum number of induced 5‐cycles that an n ‐vertex planar graph can contain.