67 citations
- University of Illinois Urbana-ChampaignUS2 papers
- Hebrew University of JerusalemIL1 paper
- Karlstad UniversitySE1 paper
- Luleå University of TechnologySE1 paper
- Royal Holloway University of LondonGB1 paper
- Universidad de LondresMX1 paper
- Universitat de BarcelonaES1 paper
- University of California San DiegoUS1 paper
- University of Southern CaliforniaUS1 paper
- U.S. National Science FoundationUS1 paper
17 papers · 1 filter
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…
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…
A spectral condition for odd cycles in graphs
Vladimir Nikiforov
We give a sharp spectral condition for the existence of odd cycles in a graph of given order. We also prove a related stability result.
Turan's theorem inverted
Vladimir Nikiforov
Turan's theorem implies that every graph of order n with more edges than the r-partite Turan graph contains a complete graph of order r+1. We show that the same premise implies the…
Ramsey Goodness and Beyond
Vladimir Nikiforov, Cecil C. Rousseau
In a seminal paper from 1983, Burr and Erdos started the systematic study of Ramsey numbers of cliques vs. large sparse graphs, raising a number of problems. In this paper we devel…