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Generalized Turán number for linear forests.
- Source :
-
Discrete Mathematics . Oct2022, Vol. 345 Issue 10, pN.PAG-N.PAG. 1p. - Publication Year :
- 2022
-
Abstract
- The generalized Turán number ex (n , K s , H) is defined to be the maximum number of copies of a complete graph K s in any H -free graph on n vertices. Let F be a linear forest consisting of k paths of orders ℓ 1 , ℓ 2 ,... , ℓ k. By characterizing the structure of the F -free graph with large minimum degree, we determine the value of ex (n , K s , F) for n = Ω (| F | s) and k ≥ 2 except some ℓ i = 3 , and the corresponding extremal graphs. Our result confirms a conjecture, due to Yuan and Zhang (2021), on classical Turán number of any linear forest for n = Ω (| F | 2) and each ℓ i ≠ 3 , and improves some known results on classical Turán number of linear forest. [ABSTRACT FROM AUTHOR]
- Subjects :
- *GRAPH algorithms
*LOGICAL prediction
*COMPLETE graphs
*RAMSEY numbers
Subjects
Details
- Language :
- English
- ISSN :
- 0012365X
- Volume :
- 345
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Discrete Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 157386396
- Full Text :
- https://doi.org/10.1016/j.disc.2022.112997