Results 11 to 20 of about 147,831 (333)
A theorem on planar graphs [PDF]
Transactions of the American Mathematical Society, 1956 W. T. Tutte
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Discrete Mathematics, 1974 AbstractA 3-valent graph G is cyclically n-connected provided one must cut at least n edges in order to separate any two circuits of G. If G is cyclically n-connected but any separation of G by cutting n edges yields a component consisting of a simple circuit, then we say that G is strongly cyclically n-connected.
David Barnette
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Historia Mathematica, 1985 In 1930 \textit{K. Kuratowski} published a proof of the ''Theorem on planar graphs'': A graph is planar if and only if it does not contain a subgraph homeomorphic to either \(K_ 5\) (the complete graph on 5 points), or \(K_{3,3}\) (the complete bipartite graph on 3,3 points).
John W. Kennedy +2 more
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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
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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
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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.
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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
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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
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The Electronic Journal of Combinatorics, 2019 We say that a graph $H$ is planar unavoidable if there is a planar graph $G$ such that any red/blue coloring of the edges of $G$ contains a monochromatic copy of $H$, otherwise we say that $H$ is planar avoidable. That is, $H$ is planar unavoidable if there is a Ramsey graph for $H$ that is planar. It follows from the Four-Color Theorem and a result of
Axenovich, M. +3 more
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Connectivity of Planar Graphs [PDF]
Journal of Graph Algorithms and Applications, 2001 We give here three simple linear time algorithms on planar graphs: a 4-connexity test for maximal planar graphs, an algorithm enumerating the triangles and a 3-connexity test. Although all these problems got already linear-time solutions, the presented algorithms are both simple and efficient. They are based on some new theoretical results.
de Fraysseix, Hubert +1 more
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