
TL;DR
This paper investigates the maximum number of copies of a graph H in an F-free graph, establishing general theorems for when F has certain chromatic properties and precisely determining extremal numbers for specific graph pairs.
Contribution
It provides a general theorem for F with an edge whose removal lowers chromatic number, and determines exact extremal numbers for certain cycles and paths.
Findings
Determines $ex(n,P_k,C_{2 ext{l}+1})$ exactly for large n.
Determines $ex(n,C_{2k},C_{2 ext{l}+1})$ exactly for large n.
Establishes a general theorem for F with an edge decreasing chromatic number.
Abstract
For graphs and , the generalized Tur\'an number is the largest number of copies of in an -free graph on vertices. We say that is -Tur\'an-good if is the number of copies in the -partite Tur\'an graph, provided is large enough. We present a general theorem in case has an edge whose deletion decreases the chromatic number. In particular, this determines and exactly, if is large enough. We also study the case when has a vertex whose deletion decreases the chromatic number.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph theory and applications · Graph Labeling and Dimension Problems
