The edit distance function of some graphs

Edit Distance in Graphs

The focus of my research is extremal graph theory and random combinatorial structures. I have also worked in a variety of other areas, including intersecting hypergraphs, the theory of positional games and Ramsey theory. I use a number of tools in my research, notably probabilistic methods and, most prominently, Szemerédi’s regularity lemma. I have used these and other techniques to address que...

Distance-Balanced Closure of Some Graphs

In this paper we prove that any distance-balanced graph $G$ with $Delta(G)geq |V(G)|-3$ is regular. Also we define notion of distance-balanced closure of a graph and we find distance-balanced closures of trees $T$ with $Delta(T)geq |V(T)|-3$.

The Edit Distance Function and Symmetrization

The edit distance between two graphs on the same labeled vertex set is the size of the symmetric difference of the edge sets. The distance between a graph, G, and a hereditary property, H, is the minimum of the distance between G and each G′ ∈ H with the same number of vertices. The edit distance function of H is a function of p ∈ [0, 1] and is the limit of the maximum normalized distance betwe...

The edit distance function and localization

The edit distance between two graphs on the same labeled vertex set is the symmetric difference of the edge sets. The distance between a graph, G, and a hereditary property, H, is the minimum of the distance between G and each G′ ∈ H. The edit distance function of H is a function of p ∈ [0, 1] and is the limit of the maximum normalized distance between a graph of density p and H. This paper dev...

Bipartite Graph Matching for Computing the Edit Distance of Graphs