Related papers: Accumulation points of the edit distance function
The chromatic threshold $\delta_\chi(H,p)$ of a graph $H$ with respect to the random graph $G(n,p)$ is the infimum over $d > 0$ such that the following holds with high probability: the family of $H$-free graphs $G \subset G(n,p)$ with…
Denote by $\mathcal{H}_k (n,p)$ the random $k$-graph in which each $k$-subset of $\{1... n\}$ is present with probability $p$, independent of other choices. More or less answering a question of Balogh, Bohman and Mubayi, we show: there is a…
In graph bootstrap percolation, edges of an Erd\H{o}s-R\'enyi random graph ${\mathcal G}_{n,p}$ are initially active. Activation spreads to other edges of the complete graph $K_n$ by an iterative process governed by a fixed graph $H$,…
We show that for every integer $k\geq3$, the set of Tur\'an densities of $k$-uniform hypergraphs has an accumulation point in $[0,1)$. In particular, $1/2$ is an accumulation point for the set of Tur\'an densities of $3$-uniform…
Graph edit distance (GED) is a powerful and flexible graph matching paradigm that can be used to address different tasks in structural pattern recognition, machine learning, and data mining. In this paper, some new binary linear programming…
The chromatic threshold $\delta_\chi(H,p)$ of a graph $H$ with respect to the random graph $G(n,p)$ is the infimum over $d > 0$ such that the following holds with high probability: the family of $H$-free graphs $G \subset G(n,p)$ with…
We consider two graph colouring problems in which edges at distance at most $t$ are given distinct colours, for some fixed positive integer $t$. We obtain two upper bounds for the distance-$t$ chromatic index, the least number of colours…
Graph Edit Distance (GED) is a widely used metric for measuring similarity between two graphs. Computing the optimal GED is NP-hard, leading to the development of various neural and non-neural heuristics. While neural methods have achieved…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
In the Cluster Editing problem, sometimes known as (unweighted) Correlation Clustering, we must insert and delete a minimum number of edges to achieve a graph in which every connected component is a clique. Owing to its applications in…
As an application of Szemeredi's regularity lemma, Erdos-Frankl-Rodl (1986) showed that the number of graphs on vertex set {1,2,...n} with a monotone class P is $2^{(1+o(1))ex(n,P)n^2/2}$ where $ex(n,P)$ is the maximum number of edges of an…
Given a graph pair $(G^1, G^2)$, graph edit distance (GED) is defined as the minimum number of edit operations converting $G^1$ to $G^2$. GED is a fundamental operation widely used in many applications, but its exact computation is NP-hard,…
The dissertation is related to combinatorial geometry with a strong probabilistic flavor. The main results can be split into three parts. The results of the first part guarantee that each "unit distance graph" in the plane has an induced…
Consider a plane graph G, drawn with straight lines. For every pair a,b of vertices of G, we compare the shortest-path distance between a and b in G (with Euclidean edge lengths) to their actual distance in the plane. The worst-case ratio…
For a given number of colors, $s$, the guessing number of a graph is the (base $s$) logarithm of the cardinality of the largest family of colorings of the vertex set of the graph such that the color of each vertex can be determined from the…
To each edge (i,j), i<j of the complete directed graph on the integers we assign unit weight with probability p or weight x with probability 1-p, independently from edge to edge, and give to each path weight equal to the sum of its edge…
The codegree Tur\'an density $\gamma(F)$ of a $k$-graph $F$ is the smallest $\gamma\in[0,1)$ such that every $k$-graph $H$ with $\delta_{k-1}(H)\geq(\gamma+o(1))\vert V(H)\vert$ contains a copy of $F$. We prove that for all…
Graph edit distance / similarity is widely used in many tasks, such as graph similarity search, binary function analysis, and graph clustering. However, computing the exact graph edit distance (GED) or maximum common subgraph (MCS) between…
Let $\mathcal{C}$ be a family of edge-colored graphs. A $t$-edge colored graph $G$ is $(\mathcal{C}, t)$-saturated if $G$ does not contain any graph in $\mathcal{C}$ but the addition of any edge in any color in $[t]$ creates a copy of some…
We prove a robust version of a graph embedding theorem of Sauer and Spencer. To state this sparser analogue, we define $G(p)$ to be a random subgraph of $G$ obtained by retaining each edge of $G$ independently with probability $p \in…