Results 21 to 30 of about 179,348 (60)
Journal of Combinatorial Theory, Series B, 1973 AbstractAn F-planar graph, where F is an ordered field, is a graph that can be represented in the plane F × F, with non-crossing line segments as edges. It is shown that the graph G is F-planar for some F if and only if every finite subgraph of G is planar.
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A Polynomial-time Algorithm for Outerplanar Diameter Improvement
, 2014 The Outerplanar Diameter Improvement problem asks, given a graph $G$ and an integer $D$, whether it is possible to add edges to $G$ in a way that the resulting graph is outerplanar and has diameter at most $D$.
Cohen, Nathann +6 more
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Bar 1-Visibility Graphs and their relation to other Nearly Planar Graphs [PDF]
, 2013 A graph is called a strong (resp. weak) bar 1-visibility graph if its vertices can be represented as horizontal segments (bars) in the plane so that its edges are all (resp.
Evans, William +5 more
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Some Results On Convex Greedy Embedding Conjecture for 3-Connected Planar Graphs
, 2009 A greedy embedding of a graph $G = (V,E)$ into a metric space $(X,d)$ is a function $x : V(G) \to X$ such that in the embedding for every pair of non-adjacent vertices $x(s), x(t)$ there exists another vertex $x(u)$ adjacent to $x(s)$ which is closer to $
A. Kelmans +13 more
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Planar L-Drawings of Directed Graphs
, 2017 We study planar drawings of directed graphs in the L-drawing standard. We provide necessary conditions for the existence of these drawings and show that testing for the existence of a planar L-drawing is an NP-complete problem.
A Garg +12 more
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, 2017 We study straight-line drawings of graphs where the vertices are placed in convex position in the plane, i.e., convex drawings. We consider two families of graph classes with nice convex drawings: outer $k$-planar graphs, where each edge is crossed by at
AWM Dress +23 more
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Strip Planarity Testing for Embedded Planar Graphs [PDF]
Algorithmica, 2016 In this paper we introduce and study the strip planarity testing problem, which takes as an input a planar graph $G(V,E)$ and a function $ :V \rightarrow \{1,2,\dots,k\}$ and asks whether a planar drawing of $G$ exists such that each edge is monotone in the $y$-direction and, for any $u,v\in V$ with $ (u)
Patrizio Angelini +3 more
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Intuitionistic Fuzzy Planar Graphs [PDF]
Discrete Dynamics in Nature and Society, 2014 Graph theory has numerous applications in modern sciences and technology. Atanassov introduced the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets. Intuitionistic fuzzy set has shown advantages in handling vagueness and uncertainty compared to fuzzy set.
N. O. Alshehri, Muhammad Akram
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Small Planar Hypohamiltonian Graphs
Journal of Graph TheoryABSTRACTA graph is hypohamiltonian if it is non‐hamiltonian, but the deletion of every single vertex gives a Hamiltonian graph. Until now, the smallest known planar hypohamiltonian graph had 40 vertices, a result due to Jooyandeh, McKay, Östergård, Pettersson, and Zamfirescu.
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Random Structures & Algorithms, 2006 AbstractWe show that the number of labeled cubic planar graphs on n vertices with n even is asymptotically αn−7/2ρ−nn!, where ρ−1 ≐ 3.13259 and α are analytic constants. We show also that the chromatic number of a random cubic planar graph that is chosen uniformly at random among all the labeled cubic planar graphs on n vertices is three with ...
Bodirsky, M +3 more
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