In the recent years, extensions of graph transformation systems with quantitative properties, such as real-time and stochastic behavior received considerable attention. In this paper, we describe the new quantitative modeling approach of probabilistic graph transformation systems (PGTSs) which incorporate probabilistic behavior into graph transformation systems. Among other applications, PGTSs ...

Given a graph G = (V,E) and a proper vertex colouring of G, a Kempe chain is a subset of V that induces a maximal connected subgraph of G in which every vertex has one of two colours. To make a Kempe change is to obtain one colouring from another by exchanging the colours of vertices in a Kempe chain. Two colourings are Kempe equivalent if each can be obtained from the other by a series of Kemp...

A biclique is a maximal induced complete bipartite subgraph of a graph. We investigate the intersection structure of edge-sets of bicliques in a graph. Specifically, we study the associated edge-biclique hypergraph whose hyperedges are precisely the edge-sets of all bicliques. We characterize graphs whose edgebiclique hypergraph is conformal (i.e., it is the clique hypergraph of its 2-section) ...

The notions of hypertree width and generalized hypertree width were introduced by Gottlob, Leone, and Scarcello in order to extend the concept of hypergraph acyclicity. These notions were further generalized by Grohe and Marx, who introduced the fractional hypertree width of a hypergraph. All these width parameters on hypergraphs are useful for extending the tractability of many problems in dat...

A user often needs training and guidance while performing several daily life procedures, e.g., cooking, setting up a new appliance, or doing COVID test. Watch-based human activity recognition (HAR) can track users' actions during these procedures. However, out of the box, state-of-the-art HAR struggles from noisy data less-expressive that are part tasks. This paper proposes PrISM-Tracker, proce...

We prove that the Covering Property Axiom CPA prism, which holds in the iterated perfect set model, implies that there exists an additive discontinuous almost continuous function f : R → R whose graph is of measure zero. We also show that, under CPA prism, there exists a Hamel basis H for which, E+(H), the set of all linear combinations of elements from H with positive rational coefficients, is...

A thrackle (resp. generalized thrackle) is a drawing of a graph in which each pair of edges meets precisely once (resp. an odd number of times). For a graph with n vertices and m edges, we show that, for drawings in the plane, m ≤ 32 (n− 1) for thrackles, while m ≤ 2n − 2 for generalized thrackles. This improves theorems of Lovász, Pach, and Szegedy. The paper also examines thrackles in the mor...

We introduce the notion of generalized Delaunay triangulation of a planar straight-line graph G = (V, E) in the Euclidean plane and present some characterizations of the triangulation. It is shown that the generalized Delaunay triangulation has the property that the minimum angle of the triangles in the triangulation is maximum among all possible triangulations of the graph. A general algorithm...