Results 271 to 280 of about 380,403 (285)

Light edges in 1‐planar graphs

Journal of Graph Theory, 2022
A graph is 1‐planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. In this paper, we prove that every 1‐planar graph G $G$ with minimum degree at least 3 contains an edge x y $xy$ with d G ( x ) ≤ d G ( y ) ${d}_ ...
Juan Liu, Yiqiao Wang, Weifan Wang
semanticscholar   +1 more source

Extending Partial 1-Planar Drawings

International Colloquium on Automata, Languages and Programming, 2020
Algorithmic extension problems of partial graph representations such as planar graph drawings or geometric intersection representations are of growing interest in topological graph theory and graph drawing.
E. Eiben, R. Ganian, Thekla Hamm, Fabian Klute, M. Nöllenburg   +4 more
semanticscholar   +1 more source

Extending Nearly Complete 1-Planar Drawings in Polynomial Time

International Symposium on Mathematical Foundations of Computer Science, 2020
The problem of extending partial geometric graph representations such as plane graphs has received considerable attention in recent years. In particular, given a graph $G$, a connected subgraph $H$ of $G$ and a drawing $\mathcal{H}$ of $H$, the extension
E. Eiben, R. Ganian, Thekla Hamm, Fabian Klute, M. Nöllenburg   +4 more
semanticscholar   +1 more source

The Book Thickness of 1-Planar Graphs is Constant

Algorithmica, 2015
In a book embedding, the vertices of a graph are placed on the “spine” of a book and the edges are assigned to “pages”, so that edges on the same page do not cross.
M. Bekos, Till Bruckdorfer, M. Kaufmann, C. Raftopoulou   +3 more
semanticscholar   +1 more source

Density of straight-line 1-planar graph drawings

Information Processing Letters, 2013
W. Didimo
semanticscholar   +1 more source

Outer 1-Planar Graphs

Algorithmica, 2016
Christopher Auer, C. Bachmaier, F. Brandenburg, Andreas Gleißner, Kathrin Hanauer, Daniel Neuwirth, Josef Reislhuber   +6 more
semanticscholar   +2 more sources

A totally (Δ + 1)-colorable 1-planar graph with girth at least five

, 2016
Lin Sun, Jian Wu, Hua Cai
semanticscholar   +1 more source

The Matching Extendability of Optimal 1-Planar Graphs

Graphs and Combinatorics, 2018
J. Fujisawa, Keita Segawa, Yusuke Suzuki
semanticscholar   +1 more source

Total coloring of outer-1-planar graphs with near-independent crossings

Journal of combinatorial optimization, 2017
Xin Zhang
semanticscholar   +1 more source

Equitable Coloring of Three Classes of 1-planar Graphs

, 2018
Xin Zhang, Huijuan Wang, Lan Xu
semanticscholar   +1 more source