Results 31 to 40 of about 713,494 (298)
Matched Drawings of Planar Graphs
Journal of Graph Algorithms and Applications, 2009 A natural way to draw two planar graphs whose vertex sets are matched is to assign each matched pair a unique y-coordinate. In this paper we introduce the concept of such matched drawings, which is a relaxation of simultaneous geometric embeddings with ...
Emilio Di Giacomo +4 more
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1-Planarity of Graphs with a Rotation System
Journal of Graph Algorithms and Applications, 2015 A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once. 1-planarity is known NP-hard, even for graphs of bounded bandwidth, pathwidth, or treewidth, and for near-planar graphs in which an edge is added to a planar
Christopher Auer +3 more
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Not all planar graphs are in PURE-4-DIR
Journal of Graph Algorithms and Applications, 2020 We prove that some planar graphs are not intersection graphs of segments if only four slopes are allowed for the segments, and if parallel segments do not intersect. This refutes a conjecture of D. West [D. West, SIAM J. Discrete Math. Newsletter, 1991].
Daniel Gonçalves
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The Electronic Journal of Combinatorics, 2018 A nonplanar graph $G$ is called almost-planar if for every edge $e$ of $G$, at least one of $G\backslash e$ and $G/e$ is planar. In 1990, Gubser characterized 3-connected almost-planar graphs in his dissertation. However, his proof is so long that only a small portion of it was published.
Guoli Ding +2 more
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The Liouville and the intersection properties are equivalent for planar graphs [PDF]
, 2012 It is shown that if a planar graph admits no non-constant bounded harmonic function then the trajectories of two independent simple random walks intersect almost ...
Itai Benjamini +5 more
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On planar hypohamiltonian graphs
Journal of Graph Theory, 2010 Summary: We present a planar hypohamiltonian graph on 42 vertices and (as a corollary) a planar hypotraceable graph on 162 vertices, improving the bounds of Zamfirescu and Zamfirescu and show some other consequences. We also settle the open problem whether there exists a positive integer \(N\), such that for every integer \(n\geq N\) there exists a ...
Wiener, Gabor, Araya, Makoto
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On Weak Flexibility in Planar Graphs [PDF]
, 2022 Recently, Dvořák, Norin, and Postle introduced flexibility as an extension of list coloring on graphs (J Graph Theory 92(3):191–206, 2019, https://doi.org/10.1002/jgt. 22447).
Murphy, Kyle +3 more
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Planar Transitive Graphs [PDF]
The Electronic Journal of Combinatorics, 2018 We prove that the first homology group of every planar locally finite transitive graph $G$ is finitely generated as an $\Aut(G)$-module and we prove a similar result for the fundamental group of locally finite planar Cayley graphs. Corollaries of these results include Droms's theorem that planar groups are finitely presented and Dunwoody's theorem that
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Recognizing IC-Planar and NIC-Planar Graphs
Journal of Graph Algorithms and Applications, 2018 We prove that triangulated IC-planar graphs and triangulated $K_5$-free or $X4W$-free NIC-planar graphs can be recognized in cubic time. A graph is 1-planar if it can be drawn in the plane with at most one crossing per edge.
Franz Brandenburg
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Coloring count cones of planar graphs [PDF]
, 2022 For a plane near‐triangulation G with the outer face bounded by a cycle C, let nG⋆ denote the function that to each 4‐coloring ψ of C assigns the number of ways ψ extends to a 4‐coloring of G.
Lidicky, Bernard, Dvořák, Zdeněk
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