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Turán number for odd‐ballooning of trees.
- Source :
-
Journal of Graph Theory . Oct2023, Vol. 104 Issue 2, p261-274. 14p. - Publication Year :
- 2023
-
Abstract
- The Turán number ex(n,H) $\text{ex}(n,H)$ is the maximum number of edges in an H $H$‐free graph on n $n$ vertices. Let T $T$ be any tree. The odd‐ballooning of T $T$, denoted by To ${T}_{o}$, is a graph obtained by replacing each edge of T $T$ with an odd cycle containing the edge, and all new vertices of the odd cycles are distinct. In this paper, we determine the exact value of ex(n,To) $\text{ex}(n,{T}_{o})$ for sufficiently large n $n$ and To ${T}_{o}$ being good, which generalizes all the known results on ex(n,To) $\text{ex}(n,{T}_{o})$ for T $T$ being a star, due to Erdős, Füredi, Gould, and Gunderson (1995), Hou, Qiu, and Liu (2018), and Yuan (2018), and provides some counterexamples with chromatic number three to a conjecture of Keevash and Sudakov (2004), on the maximum number of edges not in any monochromatic copy of H $H$ in a 2‐edge‐coloring of a complete graph of order n $n$. [ABSTRACT FROM AUTHOR]
- Subjects :
- *RAMSEY numbers
*COMPLETE graphs
*TREES
Subjects
Details
- Language :
- English
- ISSN :
- 03649024
- Volume :
- 104
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Graph Theory
- Publication Type :
- Academic Journal
- Accession number :
- 170394226
- Full Text :
- https://doi.org/10.1002/jgt.22959