Results 31 to 40 of about 11,183,836 (302)
The Crossing Numbers of Join Products of Paths and Cycles with Four Graphs of Order Five
Mathematics, 2021 The main aim of the paper is to establish the crossing numbers of the join products of the paths and the cycles on n vertices with a connected graph on five vertices isomorphic to the graph K1,1,3\e obtained by removing one edge e incident with some ...
Michal Staš
doaj +1 more source
Crossing number, pair-crossing number, and expansion
Journal of Combinatorial Theory, Series B, 2004 The crossing number \(\text{cr}(G)\) of a graph \(G\) is the minimum possible number of edge crossings in a drawing of \(G\) in the plane, and the pair-crossing number \( \text{pcr}(G)\) of a graph \(G\) is smallest number of pairs of crossing edges in any drawing of \(G\) in the plane.
Kolman, Petr, Matoušek, Jiřı́
openaire +1 more source
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].
Mohar, Bojan, Stephen, Tamon
openaire +2 more sources
Parity Properties of Configurations
Mathematics, 2022 In the paper, the crossing number of the join product G*+Dn for the disconnected graph G* consisting of two components isomorphic to K2 and K3 is given, where Dn consists of n isolated vertices.
Michal Staš
doaj +1 more source
Odd Crossing Number Is Not Crossing Number [PDF]
, 2006 The crossing number of a graph is the minimum number of edge intersections in a plane drawing of a graph, where each intersection is counted separately. If instead we count the number of pairs of edges that intersect an odd number of times, we obtain the odd crossing number. We show that there is a graph for which these two concepts differ, answering a
Michael J. Pelsmajer +2 more
openaire +1 more source
On the Pseudolinear Crossing Number [PDF]
Journal of Graph Theory, 2014 A drawing of a graph is pseudolinear if there is a pseudoline arrangement such that each pseudoline contains exactly one edge of the drawing. The pseudolinear crossing number of a graph G is the minimum number of pairwise crossings of edges in a ...
César Hernández-Vélez +2 more
semanticscholar +1 more source
Graphs and Combinatorics, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ku, Cheng Yeaw, Wong, Kok Bin
openaire +3 more sources
On the Crossing Numbers of Cartesian Products of Wheels and Trees
Discussiones Mathematicae Graph Theory, 2017 Bokal developed an innovative method for finding the crossing numbers of Cartesian product of two arbitrarily large graphs. In this article, the crossing number of the join product of stars and cycles are given.
Klešč Marián +2 more
doaj +1 more source
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
openaire +2 more sources
On the Crossing Numbers of Cartesian Products of Stars and Graphs of Order Six
Discussiones Mathematicae Graph Theory, 2013 The crossing number cr(G) of a graph G is the minimal number of crossings over all drawings of G in the plane. According to their special structure, the class of Cartesian products of two graphs is one of few graph classes for which some exact values of ...
Klešč Marián, Schrötter Štefan
doaj +1 more source