15 citations · 30 across the 15 of their papers we have counts for
32 papers · 1 filter
The maximum spectral radius of C_4-free graphs of given order and size
Vladimir Nikiforov
Let G be a graph of n vertices and m edges, and let G has no cycles of length 4. We give upper bounds on the adjacency spectral radius of G in terms of n and m.
Graphs with many copies of a given subgraph
Vladimir Nikiforov
We show that if a graph G of order n contains many copies of a given subgraph H, then it contains a blow-up of H of order log n.
Spectral saturation: inverting the spectral Turan theorem
Vladimir Nikiforov
We prove that if the spectral radius of a graph G of order n is larger than the spectral radius of the r-partite Turan graph of the same order, then G contains various supergraphs…
A spectral stability theorem for large forbidden graphs
Vladimir Nikiforov
We extend the classical stability theorem of Erdos and Simonovits in two directions: first, we allow the order of the forbidden graph to grow as log of order of the host graph, and…
Complete r-partite subgraphs of dense r-graphs
Vladimir Nikiforov
We determine how large r-partite graphs can be found in r-uniform graphs with n vertices and Cn^r edges, where C is a slowly decreasing function of n. This refines results of Erdos…
The number of cliques in graphs of given order and size
Vladimir Nikiforov
Let k_r(n,m) denote the minimum number of r-cliques in graphs with n vertices and m edges. For r=3,4 we give a lower bound on k_r(n,m) that approximates k_r(n,m) with an error smal…