Extremal graphs for odd wheels

For a graph H, the Turán number of H, denoted by ex(n,H), is the maximum number of edges of an n‐vertex H‐free graph. Let g(n,H) denote the maximum number of edges not contained in any monochromatic copy of H in a 2‐edge‐coloring of Kn. A wheel Wm is a graph formed by connecting a single vertex to a...

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Bibliographic Details
Published inJournal of graph theory Vol. 98; no. 4; pp. 691 - 707
Main Author Yuan, Long‐Tu
Format Journal Article
LanguageEnglish
Published Hoboken Wiley Subscription Services, Inc 01.12.2021
Subjects
Apexes
decomposition family
Graph coloring
Graph theory
Turán number
wheels
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ISSN0364-9024
1097-0118
DOI10.1002/jgt.22727

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Summary:For a graph H, the Turán number of H, denoted by ex(n,H), is the maximum number of edges of an n‐vertex H‐free graph. Let g(n,H) denote the maximum number of edges not contained in any monochromatic copy of H in a 2‐edge‐coloring of Kn. A wheel Wm is a graph formed by connecting a single vertex to all vertices of a cycle of length m−1. The Turán number of W2k was determined by Simonovits in 1960s. In this paper, we determine ex(n,W2k+1) when n is sufficiently large. We also show that, for sufficient large n, g(n,W2k+1)=ex(n,W2k+1) which confirms a conjecture posed by Keevash and Sudakov for odd wheels.
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ISSN:0364-9024
1097-0118
DOI:10.1002/jgt.22727