We localize and strengthen Katona’s idea of an edge-toughness to a local topological toughness. We disprove a conjecture of Katona concerning the connection between edgetoughnes...
A coloring of a graph is convex if it induces a partition of the vertices into connected subgraphs. Besides being an interesting property from a theoretical point of view, tests f...
Recently, the mesh connected trees (MCT) network has been proposed as a possible architecture for parallel computers. MCT networks are obtained by combining complete binary trees ...
Given a class of graphs F, we say that a graph G is universal for F, or F-universal, if every H ∈ F is contained in G as a subgraph. The construction of sparse universal graphs ...
Daniel Johannsen, Michael Krivelevich, Wojciech Sa...
In [13], Erd˝os et al. defined the local chromatic number of a graph as the minimum number of colors that must appear within distance 1 of a vertex. For any ∆ ≥ 2, there are ...