Results 41 to 50 of about 10,813,555 (336)
Cyclic Permutations in Determining Crossing Numbers
Discussiones Mathematicae Graph Theory, 2022 The crossing number of a graph G is the minimum number of edge crossings over all drawings of G in the plane. Recently, the crossing numbers of join products of two graphs have been studied.
Klešč Marián, Staš Michal
doaj +1 more source
Software Solution of the Algorithm of the Cyclic-Order Graph [PDF]
Acta Electrotechnica et Informatica, 2018 In this paper we describe by pseudo-code the ``Algorithm of the cyclic-order graph'', which we programmed in MATLAB 2016a and which is also possible to be executed in GNU Octave. We describe program's functionality and its use.
Štefan Berežný +2 more
doaj +1 more source
The Crossing Number of Hexagonal Graph H3,n in the Projective Plane
Discussiones Mathematicae Graph Theory, 2022 Thomassen described all (except finitely many) regular tilings of the torus S1 and the Klein bottle N2 into (3,6)-tilings, (4,4)-tilings and (6,3)-tilings.
Wang Jing +3 more
doaj +1 more source
Crossing number, pair-crossing number, and expansion
Journal of Combinatorial Theory, Series B, 2004 AbstractThe crossing number cr(G) of a graph G is the minimum possible number of edge crossings in a drawing of G in the plane, while the pair-crossing number pcr(G) is the smallest number of pairs of edges that cross in a drawing of G in the plane. While cr(G)⩾pcr(G) holds trivially, it is not known whether a strict inequality can ever occur (this ...
Petr Kolman, Jiří Matoušek
openaire +2 more sources
Crossing Numbers and Cutwidths [PDF]
Journal of Graph Algorithms and Applications, 2003 The crossing number of a graph G =( V,E), denoted by cr(G), is the smallest number of edge crossings in any drawing of G in the plane. Wee assume that the drawing is good, i.e., incident edges do not cross, two edges cross at most once and at most two edges cross in a point of the plane.
Imrich Vrto, Hristo N. Djidjev
openaire +2 more sources
The Crossing Number of Join of a Special Disconnected 6-Vertex Graph with Cycle
Mathematics, 2023 The crossing number of a graph G, cr(G), is defined as the smallest possible number of edge-crossings in a drawing of G in the plane. There are almost no results concerning crossing number of join of a disconnected 6-vertex graph with cycle. The main aim
Zongpeng Ding, Xiaomei Qian
doaj +1 more source
Proceedings of the twenty-seventh annual symposium on Computational geometry, 2011 We define a variant of the crossing number for an embedding of a graphGinto ℝ3, and prove a lower bound on it which almost implies the classical crossing lemma. We also give sharp bounds on the rectilinear space crossing numbers of pseudo-random graphs.
Alfredo Hubard, Boris Bukh
openaire +4 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
On the crossing numbers of join products of five graphs of order six with the discrete graph [PDF]
Opuscula Mathematica, 2020 The main purpose of this article is broaden known results concerning crossing numbers for join of graphs of order six. We give the crossing number of the join product \(G^{\ast} + D_n\), where the disconnected graph \(G^{\ast}\) of order six consists of ...
Michal Staš
doaj +1 more source
ON THE CROSSING NUMBER OF THE JOIN OF FIVE VERTEX GRAPH WITH THE DISCRETE GRAPH Dn [PDF]
Acta Electrotechnica et Informatica, 2017 In this paper, we show the values of crossing numbers for join products of graph G on five vertices with the discrete graph Dn and the path Pn on n vertices. The proof is done with the help of software. The software generates all cyclic permutations for
Štefan BEREŽNÝ, Michal STAŠ
doaj +1 more source