3 research outputs found
Triangles in Ks-saturated graphs with minimum degree t
For , we prove that the minimum number of triangles in an -vertex
-saturated graph with minimum degree 4 is exactly , and that there is a unique extremal
graph.
This is a triangle version of a result of
Alon, Erd\H{o}s, Holzman, and Krivelevich from 1996.
Additionally, we show that for any and , there
is a -saturated -vertex graph with minimum degree that has
copies of . This shows that
unlike the number of edges, the number
of \u27s () in a -saturated graph
is not forced to grow with the minimum degree, except for possibly in lower order terms