1‐planaredge densityA graph is 1-planar if it can be drawn in the plane such that each edge iscrossed at most once. A graph, together with a 1-planar drawing is called1-plane. Brandenburg et al. showed that th
So, we came naturally to the question of whether this bound would also be the best possible for maximal outerplanar graphs. For outerplanar graphs that are not maximal, the upper-bound n/2 is the best possible, as Fig. 1 shows. We prove a simple upper-bound for γ(G) when G is a...
5.2. Basic properties of probabilistic coloring 131 5.2.1. Properties under non-identical vertex-probabilities 131 5.2.2. Properties under identical vertex-probabilities 131 5.3. PROBABILISTIC MIN COLORING in general graphs 132 5.3.1. The complexity of probabilistic coloring 132 ...
We remark that finitely generated hyperbolic groups are always finitely presented [GH88, Chapter 4], and it follows from the work of Babson and Benjamini [BB99] that their Cayley graphs have if and only if they are one-ended. Other properties of percolation on lattices in have been investiga...
A clique is a set of pairwise adjacent vertices in a graph. We determine the maximum number of cliques in a graph for the following graph classes: (1) grap
1. Introduction The notion of a greedy chain pursuit of agents was inspired by a trail of ants headed from their nest to sources of food. The question of whether ants need to estimate geometrical properties of the underlying surface to converge to the optimal path was posed by Feynman [9]...
Therefore, understanding how quantum and classical computing resources can be leveraged together is imperative for extracting maximal utility from quantum computers. An illustration of this hybrid scheme, in the context of this work, is shown in Fig. 1. In this work, we implement the variational ...
Standard and newly designed building blocks for complex urban sites– also designated by urban archetypes - are used in this study to quantify the influence of urban forms on their energy demand and energy systems design. An energy hub, which consists on
Considering a RORI index alone, the best candidate response set is represented by a maximal positive RORI index. Therefore, the RORI index of a response plan yields a ranking of response plans for, e.g., an ongoing attack, while considering the cost of implementing and maintaining this respons...
The maximum average eccentricity of maximal planar graphs was determined in [1]. Several relations between the average eccentricity and other graph parameters, for example independence number [7], [14], domination number [7], [8], [10], [11], [12], clique number [14], Wiener index [9...