Results 291 to 294 of about 192,888 (294)

Fáry’s Theorem for 1-Planar Graphs

2012
A plane graph is a graph embedded in a plane without edge crossings. Fary’s theorem states that every plane graph can be drawn as a straight-line drawing, preserving the embedding of the plane graph. In this paper, we extend Fary’s theorem to a class of non-planar graphs.
Sheung-Hung Poon, Peter Eades, Seok-Hee Hong, Giuseppe Liotta   +3 more
openaire   +2 more sources

The Maximal 1-Planarity and Crossing Numbers of Graphs

Graphs and Combinatorics, 2021
A 1-planar graph is a graph which has a drawing on the plane such that each edge has at most one crossing. Czap and Hudak showed that every 1-planar graph with n vertices has crossing number at most $$n-2$$ .
Zhangdong Ouyang, Yuanqiu Huang, Fengming Dong   +2 more
openaire   +3 more sources

Algorithms for 1-Planar Graphs

2020
A 1-planar graph is a graph that can be embedded in the plane with at most one crossing per edge. It is known that testing 1-planarity of a graph is NP-complete. This chapter reviews the algorithmic results on 1-planar graphs. We first review a linear time algorithm for testing maximal 1-planarity of a graph if a rotation system (i.e., the circular ...
openaire   +1 more source

Remarks on the joins of 1-planar graphs

Applied Mathematics and Computation, 2019
Abstract A graph is called NIC-planar if it admits a drawing in the plane such that each edge is crossed at most once and two pairs of crossing edges share at most one 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
Zhangdong Ouyang, Jun Ge, Yichao Chen
openaire   +2 more sources