Let H be a graph on h vertices. The number of induced copies of H in a graph G is denoted
by i H (G). Let i H (n) denote the maximum of i H (G) taken over all graphs G with n vertices …

Consider integers k, ℓ such that 0⩽ ℓ⩽ k 2. Given a large graph G, what is the fraction of k‐
vertex subsets of G which span exactly ℓ edges? When G is empty or complete, and ℓ is zero …

A bound on the inducibility of cycles - ScienceDirect Skip to main contentSkip to article
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Given a hereditary family G of admissible graphs and a function λ (G) that linearly depends
on the statistics of order-κ subgraphs in a graph G, we consider the extremal problem of …

We prove several different anti-concentration inequalities for functions of independent
Bernoulli-distributed random variables. First, motivated by a conjecture of Alon, Hefetz …

A long standing open problem in extremal graph theory is to describe all graphs that
maximize the number of induced copies of a path on four vertices. The character of the …

The inducibility of a graph H measures the maximum number of induced copies of H a large
graph G can have. Generalizing this notion, we study how many induced subgraphs of fixed …

We present a sufficient condition for the stability property of extremal graph problems that
can be solved via Zykov's symmetrisation. Our criterion is stated in terms of an analytic limit …

Abstract In 1975 Pippenger and Golumbic proved that any graph on n vertices admits at
most 2 e (n/k) k induced k-cycles. This bound is larger by a multiplicative factor of 2e than the …

We prove that for each odd integer k≥ 7, every graph on n vertices without odd cycles of
length less than k contains at most (n∕ k) k cycles of length k. This extends the previous …