Web19 de dez. de 2024 · A graph is NIC-planar if it admits a drawing in the plane with at most one crossing per edge and such that two pairs of crossing edges share at most one … Web1 de dez. de 2012 · As a consequence, we generalize and improve some results obtained in [F. Bazzaro, M. Montassier, A. Raspaud, (d, 1)-Total labelling of planar graphs with large …
The Maximal 1-Planarity and Crossing Numbers of Graphs
Webbounds on the density of NIC-planar graphs are 18 5 (n 2) [15] and 16 5 (n 2) [3,11] and both bounds are known to be tight for in nitely many values of n. Outer 1-planar graphs are another subclass of 1-planar graphs. They must admit a. 2 C. Bachmaier, F. J. Brandenburg, K. Hanauer WebA graph is NIC-planar if it admits a drawing in the plane with at most one crossing per edge and such that two pairs of crossing edges share at most one common end vertex. NIC-planarity generalizes IC-planarity, which allows a vertex to be incident to at most one crossing edge, and specializes 1-planarity, which only requires at most one crossing per … how hearing occur in humans
A Structure of 1-Planar Graph and Its Applications to
Web8 de jun. de 2024 · Optimal 1-planar graphs are 4-nice, and the result is the best possible. Lemma 3 ([18]). All 3-connected 1-planar graphs are 6-nice, and the result is the best possible. To bind the linear 2-arboricity of 1-planar graphs, Liu et al.[19] established the follow-ing structural theorem: Lemma 4 ([19]). Every 1-planar graph G with D 26 can be … Web1 de mai. de 2024 · A graph is 1-planar if it can be drawn on a plane so that each edge is crossed by at most one other edge. In this paper, we first give a useful structural theorem … Web20 de abr. de 2024 · The crossing number of a graph G, denoted by cr ( G ), is the minimum value of cr ( D )’s among all drawings D of G. A drawing D of a graph is called 1- planar if each edge in D is crossed at most once. If a graph has a 1-planar drawing, then it is called 1- planar. The notion of 1-planarity was introduced in 1965 by Ringel [ 13 ], and since ... highest salary country in the world 2022