Results 21 to 30 of about 9,538,132 (298)
Crossing number of toroidal graphs [PDF]
, 2006 It is shown that if a graph of n vertices can be drawn on the torus without edge crossings and the maximum degree of its vertices is at most d, then its planar crossing number cannot exceed c_dn, where c_d is a constant depending only on d.
János Pach +3 more
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The Degenerate Crossing Number and Higher-Genus Embeddings
Journal of Graph Algorithms and Applications, 2022 If a graph embeds in a surface with $k$ crosscaps, does it always have an embedding in the same surface in which every edge passes through each crosscap at most once?
Marcus Schaefer, Daniel Štefankovič
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Complexity of Geometric k-Planarity for Fixed k
Journal of Graph Algorithms and Applications, 2021 The rectilinear local crossing number, $\mathop{\overline{\rm lcr}}(G)$, of a graph $G$ is the smallest $k$ so that $G$ has a straight-line drawing with at most $k$ crossings along each edge. We show that deciding whether $\mathop{\overline{\rm lcr}}(G)
Marcus Schaefer
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Properties of Large 2-Crossing-Critical Graphs
Journal of Graph Algorithms and Applications, 2022 A $c$-crossing-critical graph is one that has crossing number at least $c$ but each of its proper subgraphs has crossing number less than $c$. Recently, a set of explicit construction rules was identified by Bokal, Oporowski, Richter, and Salazar to ...
Drago Bokal +6 more
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On the Decay of Crossing Numbers [PDF]
Journal of Combinatorial Theory, Series B, 2007 Let \(\text{cr}(G)\) denote the crossing number of the graph \(G\). \textit{B. Richter} and \textit{C. Thomassen} [J. Comb. Theory, Ser. B 58, 217--224 (1993; Zbl 0733.05035)] conjectured that there is a constant \(c\) such that every graph \(G\) with crossing number \(k\) has an edge \(e\) such that \(\text{cr}(G-e)\geq k-c\sqrt{k}\), and showed that ...
Jacob Fox, Csaba D. Tóth
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Counting Hamiltonian Cycles in 2-Tiled Graphs
Mathematics, 2021 In 1930, Kuratowski showed that K3,3 and K5 are the only two minor-minimal nonplanar graphs. Robertson and Seymour extended finiteness of the set of forbidden minors for any surface.
Alen Vegi Kalamar +2 more
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Degenerate Crossing Numbers [PDF]
Discrete & Computational Geometry, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pach, János, Tóth, Géza
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An Ongoing Project to Improve the Rectilinear and the Pseudolinear Crossing Constants
Journal of Graph Algorithms and Applications, 2020 A drawing of a graph in the plane is pseudolinear if the edges of the drawing can be extended to doubly-infinite curves that form an arrangement of pseudolines, that is, any pair of these curves crosses precisely once.
Oswin Aichholzer +4 more
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Analogies between the Crossing Number and the Tangle Crossing Number [PDF]
The Electronic Journal of Combinatorics, 2018 Tanglegrams are special graphs that consist of a pair of rooted binary trees with the same number of leaves, and a perfect matching between the two leaf-sets. These objects are of use in phylogenetics and are represented with straight-line drawings where the leaves of the two plane binary trees are on two parallel lines and only the matching edges can ...
Robin Anderson +10 more
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On the Degenerate Crossing Number [PDF]
Discrete & Computational Geometry, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Eyal Ackerman, Rom Pinchasi
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