Results 31 to 40 of about 10,813,555 (336)
Maximum Cut Parameterized by Crossing Number [PDF]
J. Graph Algorithms Appl., 2019 Given an edge-weighted graph $G$ on $n$ nodes, the NP-hard Max-Cut problem asks for a node bipartition such that the sum of edge weights joining the different partitions is maximized.
Markus Chimani +5 more
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Expected Crossing Numbers [PDF]
Electronic Notes in Discrete Mathematics, 2011 The expected value for the weighted crossing number of a randomly weighted graph is studied. A variation of the Crossing Lemma for expectations is proved. We focus on the case where the edge-weights are independent random variables that are uniformly distributed on [0,1].
Bojan Mohar, Tamon Stephen
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Triple crossing number and double crossing braid index [PDF]
Journal of knot theory and its ramifications, 2018 Traditionally, knot theorists have considered projections of knots where there are two strands meeting at every crossing. A triple crossing is a crossing where three strands meet at a single point, such that each strand bisects the crossing.
Daishiro Nishida
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On the crossing number of join product of the discrete graph with special graphs of order five
Electronic Journal of Graph Theory and Applications, 2020 The main aim of the paper is to give the crossing number of join product G+Dn for the disconnected graph G of order five consisting of the complete graph K4 and of one isolated vertex.
Michal Staš
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ALTERNATIVE PROOF ON THE CROSSING NUMBER OF K1,1,3,N [PDF]
Acta Electrotechnica et Informatica, 2019 The main aim of the paper is to give the crossing number of join product G+Dn for the connected graph G of order five isomorphic with the complete tripartite graph K1,1,3, where Dn consists on n isolated vertices.
Michal STAS
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The crossing numbers of join products of paths with three graphs of order five [PDF]
Opuscula Mathematica, 2022 The main aim of this paper is to give the crossing number of the join product \(G^\ast+P_n\) for the disconnected graph \(G^\ast\) of order five consisting of the complete graph \(K_4\) and one isolated vertex, where \(P_n\) is the path on \(n\) vertices.
Michal Staš, Mária Švecová
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Triple-crossing number and moves on triple-crossing link diagrams [PDF]
Journal of knot theory and its ramifications, 2017 Every link in the 3-sphere has a projection to the plane where the only singularities are pairwise transverse triple points. The associated diagram, with height information at each triple point, is a triple-crossing diagram of the link.
C. Adams, J. Hoste, Martin Palmer
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On the crossing number for Kronecker product of a tripartite graph with path
AKCE International Journal of Graphs and Combinatorics, 2020 The crossing number of a graph G, Cr(G) is the minimum number of edge crossings overall good drawings of G. Among the well-known four standard graph products namely Cartesian product, Kronecker product, strong product and lexicographic product, the one ...
N. Shanthini, J. Baskar Babujee
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Degenerate Crossing Numbers [PDF]
Discrete & Computational Geometry, 2006 Let G be a graph with n vertices and e ≥ 4n edges, drawn in the plane in such a way that if two or more edges (arcs) share an interior point p ,then they must properly cross one another at p. It is shown that the number of crossing points, counted without multiplicity, is at least constant times e and that the order of magnitude of this bound cannot be
Pach, János, Tóth, Géza
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Approximating the Bundled Crossing Number
Journal of Graph Algorithms and Applications, 2022 Bundling crossings is a strategy which can enhance the readability of graph drawings. In this paper we consider good drawings, i.e., we require that any two edges have at most one common point which can be a common vertex or a crossing. Our main result is that there is a polynomial-time algorithm to compute an 8-approximation of the bundled ...
Arroyo, Alan, Felsner, Stefan
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