The connectivity index w(G) of a graph G is the sum of the weights (d(u)d(v)) of all edges uv of G, where is a real number ( = 0), and d(u) denotes the degree of the vertex u. Le...
A d-dimensional hypercube drawing of a graph represents the vertices by distinct points in {0, 1}d, such that the line-segments representing the edges do not cross. We study lower...
Pinchasi and Radoiˇci´c [11] used the following observation to bound the number of edges of a topological graph without a self-crossing cycle of length 4: if we make a list of t...
Following the decontamination metaphor for searching a graph, we introduce a cleaning process, which is related to both the chip-firing game and edge searching. Brushes (instead o...
Margaret-Ellen Messinger, Richard J. Nowakowski, P...
For graphs of bounded maximum degree, we consider acyclic t-improper colourings, that is, colourings in which each bipartite subgraph consisting of the edges between two colour cl...
Louigi Addario-Berry, Louis Esperet, Ross J. Kang,...