- Tytuł:
- The Turán number of spanning star forests
- Autorzy:
-
Zhang, Lin-Peng
Wang, Ligong
Zhou, Jiale - Tematy:
-
spanning Turán problem
star forests
Loebl-Komlós-Sós type problems - Pokaż więcej
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Powiązania:
- https://bibliotekanauki.pl/articles/59604092.pdf Link otwiera się w nowym oknie
- Opis:
- Let \( \mathcal{F} \) be a family of graphs. The Turán number of \( \mathcal{F} \), denoted by \( ex(n, \mathcal{F}) \), is the maximum number of edges in a graph with $n$ vertices which does not contain any subgraph isomorphic to some graph in \( \mathcal{F} \). A star forest is a forest whose connected components are all stars and isolated vertices. Motivated by the results of Wang, Yang and Ning about the spanning Turán number of linear forests [J. Wang and W. Yang, The Turán number for spanning linear forests, Discrete Appl. Math. 254 (2019) 291–294; B. Ning and J. Wang, The formula for Turán number of spanning linear forests, Discrete Math. 343 (2020) #111924]. In this paper, let \( \mathcal{S}_{n, k} \) be the set of all star forests with \( n \) vertices and \( k \) edges. We prove that when \( 1\le k\le n-1 \), \( ex(n,\mathcal{S}_{n, k})= \left\lfloor \frac{k^2-1}{2}\right\rfloor. \)
- Dostawca treści:
- Biblioteka Nauki
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