- Tytuł:
- Turán Function and H-Decomposition Problem for Gem Graphs
- Autorzy:
-
Liu, Henry
Sousa, Teresa - Powiązania:
- https://bibliotekanauki.pl/articles/31342280.pdf
- Data publikacji:
- 2018-08-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
gem graph
Turán function
extremal graph
graph decomposition - Opis:
- Given a graph H, the Turán function ex(n,H) is the maximum number of edges in a graph on n vertices not containing H as a subgraph. For two graphs G and H, an H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a graph isomorphic to H. Let ϕ(n,H) be the smallest number ϕ such that any graph G of order n admits an H-decomposition with at most ϕ parts. Pikhurko and Sousa conjectured that ϕ (n,H) = ex(n,H) for χ (H) ≥ 3 and all sufficiently large n. Their conjecture has been verified by Özkahya and Person for all edge-critical graphs H. In this article, we consider the gem graphs gem4 and gem5. The graph gem4 consists of the path P4 with four vertices a, b, c, d and edges ab, bc, cd plus a universal vertex u adjacent to a, b, c, d, and the graph gem5 is similarly defined with the path P5 on five vertices. We determine the Turán functions ex(n, gem4) and ex(n, gem5), and verify the conjecture of Pikhurko and Sousa when H is the graph gem4 and gem5.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2018, 38, 3; 717-741
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł