Results 11 to 20 of about 30,213,529 (145)
The structure of 1-planar graphs [PDF]
Discrete Mathematics, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Igor Fabrici, Tomás Madaras
openaire +4 more sources
k-L(2, 1)-labelling for planar graphs is NP-complete for k>=4 [PDF]
, 2009 A mapping from the vertex set of a graph G=(V,E) into an interval of integers {0,...,k} is an L(2,1)-labelling of G of span k if any two adjacent vertices are mapped onto integers that are at least 2 apart, and every two vertices with a common ...
Noble, Steven +8 more
core +7 more sources
Cops and Robbers on 1-Planar Graphs
, 2023 Cops and Robbers is a well-studied pursuit-evasion game in which a set of cops seeks to catch a robber in a graph G, where cops and robber move along edges of G. The cop number of G is the minimum number of cops that is sufficient to catch the robber. Every planar graph has cop number at most three, and there are planar graphs for which three cops are ...
Stephane Durocher +8 more
openaire +5 more sources
On the Density of Maximal 1-Planar Graphs [PDF]
, 2013 A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once. It is maximal 1-planar if the addition of any edge violates 1-planarity. Maximal 1-planar graphs have at most 4n−8 edges. We show that there are sparse maximal 1-planar graphs with only $\frac{45}{17} n + \mathcal{O}(1)$ edges.
Franz-Josef Brandenburg +5 more
openaire +2 more sources
Unique Triangulated 1-Planar Graphs
CoRR, 2023 It is well-known that every 3-connected planar graph has a unique planar embedding on the sphere. We study the extension to triangulated 1-planar graphs, T1P graphs for short, which admit an embedding in which each edge is crossed at most once and each face is a triangle, and obtain an algorithmic solution by a cubic time recognition algorithm that ...
Brandenburg, Franz J.
openaire +3 more sources
On RAC drawings of 1-planar graphs
Theoretical Computer Science, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bekos, Michael A. +4 more
openaire +3 more sources
Minimal non-1-planar graphs [PDF]
Discrete Mathematics, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Korzhik, Vladimir P.
openaire +3 more sources
The nonsolvability by radicals of generic 3-connected planar Laman graphs. [PDF]
, 2007 We show that planar embeddable -connected Laman graphs are generically non-soluble. A Laman graph represents a configuration of points on the Euclidean plane with just enough distance specifications between them to ensure rigidity.
Power, Stephen C., Owen, J. C.
core +4 more sources
On edge colorings of 1-planar graphs [PDF]
Information Processing Letters, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xin Zhang 0017, Jianliang Wu 0001
openaire +1 more source
On Drawings and Decompositions of 1-Planar Graphs [PDF]
The 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 tight.
Július Czap, Dávid Hudák
openaire +2 more sources