- Tytuł:
- Singular Turán Numbers and Worm-Colorings
- Autorzy:
-
Gerbner, Dániel
Patkós, Balázs
Vizer, Máté
Tuza, Zsolt - Powiązania:
- https://bibliotekanauki.pl/articles/32222590.pdf
- Data publikacji:
- 2022-11-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
Turán number
WORM-coloring
singular Turán numbers - Opis:
- A subgraph G of H is singular if the vertices of G either have the same degree in H or have pairwise distinct degrees in H. The largest number of edges of a graph on n vertices that does not contain a singular copy of G is denoted by TS(n, G). Caro and Tuza in [Singular Ramsey and Turán numbers, Theory Appl. Graphs 6 (2019) 1–32] obtained the asymptotics of TS(n, G) for every graph G, but determined the exact value of this function only in the case G = K3 and n ≡ 2 (mod 4). We determine TS(n, K3) for all n ≡ 0 (mod 4) and n ≡ 1 (mod 4), and also TS(n, Kr+1) for large enough n that is divisible by r. We also explore the connection to the so-called G-WORM colorings (vertex colorings without rainbow or monochromatic copies of G) and obtain new results regarding the largest number of edges that a graph with a G-WORM coloring can have.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2022, 42, 4; 1061-1074
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł