The exact minimum number of triangles in graphs with given order and size
H Liu, O Pikhurko, K Staden - Forum of Mathematics, Pi, 2020 - cambridge.org
What is the minimum number of triangles in a graph of given order and size? Motivated by
earlier results of Mantel and Turán, Rademacher solved the first nontrivial case of this …
earlier results of Mantel and Turán, Rademacher solved the first nontrivial case of this …
Embedding graphs into larger graphs: results, methods, and problems
M Simonovits, E Szemerédi - Building Bridges II: Mathematics of László …, 2019 - Springer
Abstract Extremal Graph Theory is a very deep and wide area of modern combinatorics. It is
very fast developing, and in this long but relatively short survey we select some of those …
very fast developing, and in this long but relatively short survey we select some of those …
A spectral Erdős-Rademacher theorem
Y Li, L Lu, Y Peng - Advances in Applied Mathematics, 2024 - Elsevier
A classical result of Erdős and Rademacher (1955) indicates a supersaturation
phenomenon. It says that if G is a graph on n vertices with at least⌊ n 2/4⌋+ 1 edges, then G …
phenomenon. It says that if G is a graph on n vertices with at least⌊ n 2/4⌋+ 1 edges, then G …
Supersaturation for subgraph counts
The classical extremal problem is that of computing the maximum number of edges in an F-
free graph. In particular, Turán's theorem entirely resolves the case where F= K r+ 1. Later …
free graph. In particular, Turán's theorem entirely resolves the case where F= K r+ 1. Later …
[HTML][HTML] Contraction and deletion blockers for perfect graphs and H-free graphs
We study the following problem: for given integers d, k and graph G, can we reduce some
fixed graph parameter π of G by at least d via at most k graph operations from some fixed set …
fixed graph parameter π of G by at least d via at most k graph operations from some fixed set …
Structure and supersaturation for intersecting families
The extremal problems regarding the maximum possible size of intersecting families of
various combinatorial objects have been extensively studied. In this paper, we investigate …
various combinatorial objects have been extensively studied. In this paper, we investigate …
[HTML][HTML] Unified approach to the generalized Turán problem and supersaturation
In this paper we introduce a unifying approach to the generalized Turán problem and
supersaturation results in graph theory. The supersaturation-extremal function satex (n, F: m …
supersaturation results in graph theory. The supersaturation-extremal function satex (n, F: m …
Spectral supersaturation: Triangles and bowties
Y Li, L Feng, Y Peng - arXiv preprint arXiv:2407.04950, 2024 - arxiv.org
Recently, Ning and Zhai (2023) proved that every $ n $-vertex graph $ G $ with $\lambda
(G)\ge\sqrt {\lfloor n^ 2/4\rfloor} $ has at least $\lfloor n/2\rfloor-1$ triangles, unless $ G= K …
(G)\ge\sqrt {\lfloor n^ 2/4\rfloor} $ has at least $\lfloor n/2\rfloor-1$ triangles, unless $ G= K …
A spectral Erd\H {o} s-Rademacher theorem
Y Li, L Lu, Y Peng - arXiv preprint arXiv:2406.05609, 2024 - arxiv.org
A classical result of Erd\H {o} s and Rademacher (1955) indicates a supersaturation
phenomenon. It says that if $ G $ is a graph on $ n $ vertices with at least $\lfloor {n …
phenomenon. It says that if $ G $ is a graph on $ n $ vertices with at least $\lfloor {n …
A spectral Erd\H {o} s-Faudree-Rousseau theorem
Y Li, L Feng, Y Peng - arXiv preprint arXiv:2406.13176, 2024 - arxiv.org
A well-known theorem of Mantel states that every $ n $-vertex graph with more than $\lfloor
n^ 2/4\rfloor $ edges contains a triangle. An interesting problem in extremal graph theory …
n^ 2/4\rfloor $ edges contains a triangle. An interesting problem in extremal graph theory …