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 there are maximal 1-planar graphs withonly $\\frac{45}{17}n + O(1)\...
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...
On the Maximal Distance Between the Centers of Mass of a Planar Convex Body and Its Boundary doi:10.1007/s00454-024-00650-0Convex bodyCenter of massExtremal problemWe prove that the length of the projection of the vector joining the centers of mass of a convex body on the plane and of ...
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...
that their cayley graphs have \(p_u<1\) if and only if they are one-ended. other properties of percolation on lattices in \(\mathbb {h}^d\) have been investigated in [ cza12 , cza18 , lal01 ]. previous progress on conjectures 1.1 and 1.2 can be briefly summarised as follows. ...
B. Andreas Graphs with unique maximal clumpings J. Graph Theory, 2 (1) (1978), pp. 19-24 Google Scholar Arnautov, 1974 V.I. Arnautov Estimation of the exterior stability number of a graph by means of the minimal degree of the vertices (in Russian) Prikl. Mat. i Programmirovanie V...