Results 1 to 10 of about 201,122 (180)
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
Untangling a Planar Graph [PDF]
Discrete & Computational Geometry, 2009 A straight-line drawing $ $ of a planar graph $G$ need not be plane, but can be made so by \emph{untangling} it, that is, by moving some of the vertices of $G$. Let shift$(G, )$ denote the minimum number of vertices that need to be moved to untangle $ $. We show that shift$(G, )$ is NP-hard to compute and to approximate. Our hardness results extend
Xavier Goaoc +5 more
openaire +5 more sources
Theoretical Computer Science, 2018 We introduce the family of $k$-gap-planar graphs for $k \geq 0$, i.e., graphs that have a drawing in which each crossing is assigned to one of the two involved edges and each edge is assigned at most $k$ of its crossings. This definition is motivated by applications in edge casing, as a $k$-gap-planar graph can be drawn crossing-free after introducing ...
Sang Won Bae +10 more
openaire +6 more sources
Mathematical Modelling and Control, 2021 In this paper, we study the problem of partitioning the vertex set of a planar graph with girth restriction into parts, also referred to as color classes, such that each part induces a graph with components of bounded order.
Chunyu Tian, Lei Sun
doaj +1 more source
Planarity of Streamed Graphs [PDF]
Theoretical Computer Science, 2015 In this paper we introduce a notion of planarity for graphs that are presented in a streaming fashion. A $\textit{streamed graph}$ is a stream of edges $e_1,e_2,...,e_m$ on a vertex set $V$. A streamed graph is $ω$-$\textit{stream planar}$ with respect to a positive integer window size $ω$ if there exists a sequence of planar topological drawings $Γ_i$
Da Lozzo G., Rutter I.
openaire +5 more sources
On the planarity of line Mycielskian graph of a graph
Ratio Mathematica, 2020 The line Mycielskian graph of a graph G, denoted by Lμ(G) is defined as the graph obtained from L(G) by adding q+1 new vertices E' = ei' : 1 ≤ i ≤ q and e, then for 1 ≤ i ≤ q , joining ei' to the neighbours of ei and to e.
Keerthi G. Mirajkar +1 more
doaj +1 more source
The k-subconnectedness of planar graphs
AIMS Mathematics, 2021 A graph G with at least 2k vertices is called k-subconnected if, for any 2k vertices x1,x2,⋯,x2k in G, there are k independent paths joining the 2k vertices in pairs in G.
Zongrong Qin, Dingjun Lou
doaj +1 more source
Tropically planar graphs [PDF]
Collectanea Mathematica, 2021 28 pages, 29 figures; updated to correct erroneous counts at the end of Section ...
Desmond Coles +4 more
openaire +3 more sources
Planar Graphs as VPG-Graphs [PDF]
Journal of Graph Algorithms and Applications, 2013 A graph is Bk-VPG when it has an intersection representation by paths in a rectangular grid with at most k bends (turns). It is known that all planar graphs are B3-VPG and this was conjectured to be tight. We disprove this conjecture by showing that all planar graphs are B2-VPG.
Steven Chaplick, Torsten Ueckerdt
openaire +4 more sources