On universality of graphs with uniformly distributed edges
Discrete Mathematics
A local density condition for triangles
Discrete Mathematics - Special issue on graph theory and applications
On the edge distribution in triangle-free graphs
Journal of Combinatorial Theory Series B
The local density of triangle-free graphs
Discrete Mathematics
Extremal Graph Theory
Edge Distribution of Graphs with Few Copies of a Given Graph
Combinatorics, Probability and Computing
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We investigate a graph function which is related to the local density, the maximal cut and the least eigenvalue of a graph. In particular it enables us to prove the following assertions.Let p ≥ 3 be an integer, c ∈ (0, 1/2) and G be a Kp-free graph on n vertices with e ≤ cn2 edges. There exists a positive constant α = α (c, p) such that:(a) some ⌊n/2⌋-subset of V (G) induces at most (c-4 − α) n2 edges (this answers a question of Paul Erdös);(b) G can be made bipartite by the omission of at most (c-2 − α) n2 edges.