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Extremal graphs for the k ‐flower
Author(s) -
Yuan LongTu
Publication year - 2018
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.22237
Subject(s) - combinatorics , mathematics , lemma (botany) , graph , vertex (graph theory) , induced subgraph , discrete mathematics , botany , poaceae , biology
The Turán number of a graph H , e x ( n , H ) , is the maximum number of edges in any graph of order n that does not contain an H as a subgraph. A graph on 2 k + 1 vertices consisting of k triangles that intersect in exactly one common vertex is called a k ‐fan, and a graph consisting of k cycles that intersect in exactly one common vertex is called a k ‐flower. In this article, we determine the Turán number of any k ‐flower containing at least one odd cycle and characterize all extremal graphs provided n is sufficiently large. Erdős, Füredi, Gould, and Gunderson determined the Turán number for the k ‐fan. Our result is a generalization of their result. The addition aim of this article is to draw attention to a powerful tool, the so‐called progressive induction lemma of Simonovits.