39 citations · 203 across the 85 of their papers we have counts for
6 papers · 1 filter
On the sum of k largest singular values of graphs and matrices
Vladimir Nikiforov
In the recent years, the trace norm of graphs has been extensively studied under the name of graph energy. The trace norm is just one of the Ky Fan k-norms, given by the sum of the…
Extremal norms of graphs and matrices
Vladimir Nikiforov
In the recent years, the trace norm of graphs has been extensively studied under the name of graph energy. In this paper some of this research is extended to more general matrix no…
The number of graphs with large forbidden subgraphs
Bela Bollobas, Vladimir Nikiforov
In this note, extending some results of Erdos, Frankl, Rodl, Alexeev, Bollobas and Thomason we determine asymptotically the number of graphs which do not contain certain large subg…
A new type of Ramsey-Turan problems
Hao Li, Vladimir Nikiforov, Richard Schelp
We introduce and study a new type of Ramsey-Turan problems, a typical example of which is the following one: let c>0 and G be a graph of sufficiently large order n with minimum deg…
Large joints in graphs
Bela Bollobas, Vladimir Nikiforov
We show that if G is a graph of sufficiently large order n containing as many r-cliques as the r-partite Turan graph of order n; then for some C>0 G has more than Cn^(r-1) (r+1)-cl…
Chromatic number and mimimum degree of K_r-free graphs
Vladimir Nikiforov
A number of famous results about triangle-free graphs determine the maximum chromatic number of graphs of order n with minimum degree greater than n/3. In this note these results a…