Results 21 to 30 of about 380,403 (285)
Orthogonal and Smooth Orthogonal Layouts of 1-Planar Graphs with Low Edge Complexity
International Symposium Graph Drawing and Network Visualization, 2018 While orthogonal drawings have a long history, smooth orthogonal drawings have been introduced only recently. So far, only planar drawings or drawings with an arbitrary number of crossings per edge have been studied. Recently, a lot of research effort in
Evmorfia N. Argyriou +7 more
openalex +3 more sources
On total colorings of 1-planar graphs [PDF]
arXiv, 2013 A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we confirm the total-coloring conjecture for 1-planar graphs with maximum degree at least 13.
Xin Zhang, Jianfeng Hou, G. Liu
arxiv +2 more sources
3D Visibility Representations of 1-planar Graphs
International Symposium Graph Drawing and Network Visualization, 2017 We prove that every 1-planar graph G has a z-parallel visibility representation, i.e., a 3D visibility representation in which the vertices are isothetic disjoint rectangles parallel to the xy-plane, and the edges are unobstructed z-parallel visibilities
Patrizio Angelini +3 more
openalex +3 more sources
On local properties of 1-planar graphs with high minimum degree
Ars Math. Contemp., 2011 A graph is called 1-planar if there exists its drawing in the plane such that each edge contains at most one crossing. We prove that each 1-planar graph of minimum degree 7 contains a pair of adjacent vertices of degree 7 as well as several small graphs ...
David E. Hudak, Tomáš Madaras
openalex +3 more sources
On the lightness of chordal 4-cycle in 1-planar graphs with high minimum degree
Ars Math. Contemp., 2013 A graph G is 1 -planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. The family of 1-planar graphs with minimum vertex degree at least δ and minimum edge degree at least ɛ is denoted by P δ 1 ( ɛ ) .
Xin Zhang, Guizhen Liu
openalex +3 more sources
On Drawings and Decompositions of 1-Planar Graphs [PDF]
Electronic Journal of Combinatorics, 2013 A graph is called 1-planar if it can be drawn in the plane so that each of its edges is crossed by at most one other edge. We show that every 1-planar drawing of any 1-planar graph on $n$ vertices has at most $n-2$ crossings; moreover, this bound is ...
Július Czap, David E. Hudak
openalex +2 more sources
Acyclic edge coloring of triangle-free 1-planar graphs [PDF]
, 2015 Wen Yao Song, Lian Ying Miao
openalex +2 more sources
On the Size of Matchings in 1-Planar Graph with High Minimum Degree [PDF]
SIAM Journal on Discrete Mathematics, 2022 A matching of a graph is a set of edges without common end vertex. A graph is called 1-planar if it admits a drawing in the plane such that each edge is crossed at most once.
Yuanqiu Huang, Zhangdong Ouyang, F. Dong
semanticscholar +1 more source
The structure and the list 3-dynamic coloring of outer-1-planar graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 An outer-1-planar graph is a graph admitting a drawing in the plane so that all vertices appear in the outer region of the drawing and every edge crosses at most one other edge.
Yan Li, Xin Zhang
doaj +1 more source
Improved product structure for graphs on surfaces [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 Dujmovi\'c, Joret, Micek, Morin, Ueckerdt and Wood [J. ACM 2020] proved that for every graph $G$ with Euler genus $g$ there is a graph $H$ with treewidth at most 4 and a path $P$ such that $G\subseteq H \boxtimes P \boxtimes K_{\max\{2g,3\}}$. We improve
Marc Distel +3 more
doaj +1 more source