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Extremal C 4 ‐Free/ C 5 ‐Free Planar Graphs
Author(s) -
Dowden Chris
Publication year - 2016
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.21991
Subject(s) - combinatorics , mathematics , planar graph , planar , graph , outerplanar graph , book embedding , discrete mathematics , 1 planar graph , pathwidth , chordal graph , line graph , computer science , computer graphics (images)
We study the topic of “extremal” planar graphs, definingexP( n , H )to be the maximum number of edges possible in a planar graph on n vertices that does not contain a given graph H as a subgraph. In particular, we examine the case when H is a small cycle, obtainingexP( n , C 4 ) ≤ 15 7 ( n − 2 )for all n ≥ 4 andexP( n , C 5 ) ≤ 12 n − 33 5for all n ≥ 11 , and showing that both of these bounds are tight.