Combinatorial group

Diana's research interests lie in extremal graph theory, Ramsey theory, probabilistic method, and limits of graphs. In particular together with Komlós, Hladký, Simonovits, Stein, and Szemerédi, she used a generalisation of the regularity lemma to sparse graphs to assymptotically solve a cojecture of Loebl, Komlós and Sós on trees. Together with Böttcher, Hladký and Taraz, she used the Rödl nibble method to make significant progress on a conjecture of Gyárfás about packing trees. |

My research is in the area of Spectral Graph Theory. I am interested in understanding how eigenvectors portray the structure of networks, such as community formation, connectivity, partitioning, etc. Besides, I conduct research on extremal problems in Spectral Graph Theory, such as characterizing graphs that achieve extremal values of algebraic connectivity, energy, etc. Spectral techniques have been used for decades to successfully reveal the underlying properties of graphs. From graphs with a specific design to random graphs, and from finite to infinite graphs, I have been applying semidefinite optimization, probability theory, and matrix theory to expose such properties. |

Until recently my main research areas have been Computational Geometry and Graph Drawing, with an emphasis on proximity graphs and Voronoi diagrams, visibility and interval graphs. Recently I have also become interested in Extremal Graph Theory and I have started to work on problems involving graph tilings. In this kind of problems, we aim to provide necessary conditions guaranteeing that some host graph G contains a fixed number of copies of another graph H. |

My main interests are random discrete structures and tail probability inequalities. I have contributed to progress on the Kim-Vu Sandwich Conjecture (and its extension to random hypergraphs) and the Upper Tail Problem for subgraph counts in the random graph G(n,p). Moreover, I have applied results of extremal hypergraph theory to obtain some optimal tail inequalities for sums of independent random variables. |