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A survey of graphs with known or bounded crossing numbers - MaRDI portal

A survey of graphs with known or bounded crossing numbers (Q5139701)

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scientific article; zbMATH DE number 7283887

Language	Label	Description	Also known as
English	A survey of graphs with known or bounded crossing numbers	scientific article; zbMATH DE number 7283887

Statements

scholarly article

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Michael Haythorpe

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publication date

10 December 2020

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full work available at URL

https://arxiv.org/abs/1901.05155

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http://ajc.maths.uq.edu.au/pdf/78/ajc_v78_p209.pdf

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zbMATH Keywords

planar crossing numbers

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graph products

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describes a project that uses

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MaRDI profile type

MaRDI publication profile

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arXiv classification

math.CO

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On topological graphs with at most four crossings per edge

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Arrangements, circular arrangements and the crossing number of \(C_{7} \times C_{n}\).

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Proofs from THE BOOK

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Crossing-Free Subgraphs

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A group-theoretic model for symmetric interconnection networks

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Crossings, colorings, and cliques

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The crossing number ofK1,3,n andK2,3,n

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Closing in on Hill's Conjecture

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Towards the Albertson conjecture

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On the crossing numbers of products of cycles and graphs of order four

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The early history of the brick factory problem

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Permutation Groups, Complexes, and Rearrangeable Connecting Networks

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On the crossing numbers of Cartesian products with paths

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On the crossing numbers of Cartesian products with trees

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An ILP-based Proof System for the Crossing Number Problem

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Augmented cubes

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Zarankiewicz's conjecture is finite for each fixed \(m\)

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An effective crossing minimisation heuristic based on star insertion

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Self-dual configurations and regular graphs

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Improved Bounds for the Crossing Numbers of Km,n and Kn

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Reduction of symmetric semidefinite programs using the regular \(\ast\)-representation

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The crossing number of c<sub>4</sub> × c<sub>4</sub>

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The crossing numbers of join of some graphs with \(n\) isolated vertices

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The crossing number of G ▭ C n for the graph G on six vertices

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On the crossing numbers of G□ Cn for graphs G on six vertices

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Crossing Number Problems

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The crossing numbers of some generalized Petersen graphs.

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An improved upper bound on the crossing number of the hypercube

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Crossing Number is NP-Complete

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On Crossing Numbers of Complete Tripartite and Balanced Complete Multipartite Graphs

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The crossing number ofCm �Cn is as conjectured forn ?m(m + 1)

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On the Möbius Ladders

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The crossing number of the complement of a circuit

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On the Number of Crossings in a Complete Graph

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Über die Kreuzungszahl vollständiger, <i>n</i>‐geteilter Graphen

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ON THE CROSSING NUMBER OF THE CARTESIAN PRODUCT OF A SUNLET GRAPH AND A STAR GRAPH

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The crossing number of \(C(3k+1;\{1,k\})\)

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The crossing number of \(K_{1,m,n}\)

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On the crossing number of some complete multipartite graphs

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The crossing number of \(K_{1,4,n}\)

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Infinite Families of Nontrivial Trivalent Graphs Which are Not Tait Colorable

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Crossing numbers of Sierpiński‐like graphs

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The crossing number of K5,n

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The crossing numbers of products of paths and stars with 4‐vertex graphs

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The crossing numbers of certain Cartesian products

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The crossing numbers of products of a 5-vertex graph with paths and cycles

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On the crossing numbers of products of stars and graphs of order five

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The crossing numbers of Cartesian products of paths with 5-vertex graphs

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The crossing number of \(K_{2,3}{\times}C_{3}\)

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Some crossing numbers of products of cycles

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The Join of Graphs and Crossing Numbers

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On the Crossing Numbers of Cartesian Products of Stars and Graphs on Five Vertices

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The crossing numbers of join of the special graph on six vertices with path and cycle

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The crossing numbers of products of 5-vertex graphs with cycles

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The crossing number of \(P^2_n \square C_3\)

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The crossing numbers of products of path with graphs of order six

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On the crossing numbers of Cartesian products of wheels and trees

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The crossing number ofC5 �Cn

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The crossing numbers of join products of paths with graphs of order four

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On the crossing numbers of Cartesian products of stars and graphs of order six

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New lower bound techniques for VLSI

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The crossing number of \(C(mk;\{1,k\})\)

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The crossing numbers of generalized Petersen graphs with small order

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The crossing number of the circular graph \(C(2m+2,m)\)

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Bounds for the crossing number of the <i>N</i>‐cube

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On the crossing number of \(K_{13}\)

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On the crossing numbers of certain generalized Petersen graphs

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An improvement of the crossing number bound

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On the crossing number of \(K_{m,n}\)

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Coloring graphs with crossings

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&lt;italic&gt;K&lt;/italic&gt;&lt;sub&gt;1,1,&lt;italic&gt;m&lt;/italic&gt;&lt;/sub&gt;□&lt;italic&gt;P&lt;/italic&gt;&lt;sub&gt;&lt;italic&gt;n&lt;/italic&gt;&lt;/sub&gt; 的交叉数

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The crossing number of the Cartesian product of paths with complete graphs

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The crossing number of join of the generalized Petersen graph \(P(3, 1)\) with path and cycle

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Improving the crossing lemma by finding more crossings in sparse graphs

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Graphs drawn with few crossings per edge

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The crossing number of <i>K</i><sub>11</sub> is 100

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The crossing number of \(P(N,3)\)

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Intersections of curve systems and the crossing number of \(C_ 5\times C_ 5\)

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The crossing number of \(C_3\times C_n\)

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THE MINIMUM NUMBER OF INTERSECTIONS IN COMPLETE GRAPHS

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Infinite families of crossing-critical graphs with given average degree

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A lower bound for the crossing number ofCm � Cn

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On the crossing numbers of loop networks and generalized Petersen graphs

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An improved bound for the crossing number of \(C_m\times C_n\): a self-contained proof using mostly combinatorial arguments

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The graph crossing number and its variants: a survey

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Crossing Numbers of Graphs

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Intersection of curves and crossing number of \(C_m\times C_n\) on surfaces

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DETERMINING CROSSING NUMBERS OF GRAPHS OF ORDER SIX USING CYCLIC PERMUTATIONS

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Determining crossing number of join of the discrete graph with two symmetric graphs of order five

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On crossing numbers of hypercubes and cube connected cycles

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The crossing number of Cartesian products of complete bipartite graphs \(K_{2,m}\) with paths \(P_{n}\)

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An upper bound for the crossing number of augmented cubes

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The crossing number of folded hypercubes

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The crossing number of the hexagonal graph \(H_{3,n}\)

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The crossing number of Cartesian product of 5-wheel with any tree

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A theorem on tait colorings with an application to the generalized Petersen graphs

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Cyclic‐order graphs and Zarankiewicz's crossing‐number conjecture

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The locally twisted cubes

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The crossing number of \(C(n; \{1,3\})\)

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The crossing number of pancake graph $P_4$ is six

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The crossing number of \(C(8,2)\square P_{n}\)

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On a problem of P. Turan concerning graphs

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On the crossing number of \(K_{ m } \square P_{n}\)

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On the crossing numbers of \(K_m\square C_n\) and \(K_{m,l}\square P_n\)

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一个特殊6点图Q与nK_{1}, P_{n}及C_{n}的联图交叉数

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Identifiers

zbMATH Open document ID

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:5139701

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