Abstract
AbstractPopielarz, Sahasrabuddhe and Snyder in 2018 proved that maximal $$K_{r+1}$$
K
r
+
1
-free graphs with $$(1-\frac{1}{r})\frac{n^2}{2}-o(n^{\frac{r+1}{r}})$$
(
1
-
1
r
)
n
2
2
-
o
(
n
r
+
1
r
)
edges contain a complete r-partite subgraph on $$n-o(n)$$
n
-
o
(
n
)
vertices. This was very recently extended to odd cycles in place of $$K_3$$
K
3
by Wang, Wang, Yang and Yuan. We further extend it to some other 3-chromatic graphs, and obtain some other stability results along the way.
Funder
Nemzeti Kutatási Fejlesztési és Innovációs Hivatal
ELKH Alfréd Rényi Institute of Mathematics
Publisher
Springer Science and Business Media LLC
Subject
Discrete Mathematics and Combinatorics,Theoretical Computer Science
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