To load a web page, a browser must fetch and evaluate objects like HTML files and JavaScript source code. Evaluating an object can result in additional objects being fetched and evaluated. Thus, loading a web page requires a browser to resolve a dependency graph; this partial ordering constrains the sequence in which a browser can process individual objects. Unfortunately, many edges in a page’...

Purse-string healing is driven by contraction of actin/myosin cables that span cells at wound edges, and it is the predominant mode of closing small round wounds in embryonic and some adult epithelia. Wounds can also heal by cell crawling, and my colleagues and I have shown previously that the presence of unconstrained, straight edges in sheets of epithelial cells is a sufficient signal to indu...

The congested clique model is a message-passing model of distributed computation where the underlying communication network is the complete graph of n nodes. In this paper we consider the situation where the joint input to the nodes is an nnode labeled graph G, i.e., the local input received by each node is the indicator function of its neighborhood in G. Nodes execute an algorithm, communicati...

Factor and Merz [Discrete Appl. Math. 159 (2011), 100–103] defined the (1, 2)-step competition graph and studied the (1, 2)-step competition graph of a tournament. In this paper, a sufficient and necessary condition for any two vertices to be adjacent in the (1, 2)-step competition graph C1,2(D) of a round digraph D is given. 1 Terminology and Introduction The competition graph of a digraph, in...

The latest achievements in 2-dimensional (2D) material research have shown the perspective use of sandwich structures in nanodevices. We demonstrate the following generation of bilayer materials for electronics and optoelectronics. The atomic structures, the stability and electronic properties of Moiré graphene (G)/h-BN bilayers with folded nanoholes have been investigated theoretically by ab-i...

(joint work with Aart Blokhuis, András Gyárfás and Miklós Ruszinkó) For positive integers k ≤ n and t let χ t (k, n) denote the minimum number of colors such that at least in one of the total t colorings of edges of K n all k 2 edges of every K k ⊆ K n get different colors. Generalizing a result of Körner and Simonyi, it is shown in this paper that χ t (3, n) = Θ(n 1/t). Also two-round coloring...

The shortest augmenting path technique is one of the fundamental ideas used in maximum matching and flow algorithms. Since being introduced by Edmonds Karp 1972, it has been widely applied many different settings. Surprisingly, despite this extensive usage, still not well understood even simplest case: online bipartite problem on trees. In a tree T=(W⊎B,E) revealed online, i.e., each round vert...