Results 21 to 30 of about 10,813,555 (336)

Towards Better Approximation of Graph Crossing Number [PDF]

open access: yesIEEE Annual Symposium on Foundations of Computer Science, 2020
Graph Crossing Number is a fundamental and extensively studied problem with wide ranging applications. In this problem, the goal is to draw an input graph $G$ in the plane so as to minimize the number of crossings between the images of its edges.
Julia Chuzhoy, S. Mahabadi, Zihan Tan
semanticscholar   +1 more source

Counting Hamiltonian Cycles in 2-Tiled Graphs

open access: yesMathematics, 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
doaj   +1 more source

On the crossing numbers of join products of W_{4}+P_{n} and W_{4}+C_{n} [PDF]

open access: yesOpuscula Mathematica, 2021
The crossing number \(\mathrm{cr}(G)\) of a graph \(G\) is the minimum number of edge crossings over all drawings of \(G\) in the plane. The main aim of the paper is to give the crossing number of the join product \(W_4+P_n\) and \(W_4+C_n\) for the ...
Michal Staš, Juraj Valiska
doaj   +1 more source

The crossing numbers of join products of four graphs of order five with paths and cycles [PDF]

open access: yesOpuscula Mathematica, 2023
The crossing number \(\mathrm{cr}(G)\) of a graph \(G\) is the minimum number of edge crossings over all drawings of \(G\) in the plane. In the paper, we extend known results concerning crossing numbers of join products of four small graphs with paths ...
Michal Staš, Mária Timková
doaj   +1 more source

The crossing numbers of join products of eight graphs of order six with paths and cycles

open access: yesKarpatsʹkì Matematičnì Publìkacìï, 2023
The crossing number $\mathrm{cr}(G)$ of a graph $G$ is the minimum number of edge crossings over all drawings of $G$ in the plane. The main aim of this paper is to give the crossing numbers of the join products of eight graphs on six vertices with paths ...
M. Staš
doaj   +1 more source

The crossing number of the generalized Petersen graph P(3k,k) in the projective plane

open access: yesAKCE International Journal of Graphs and Combinatorics, 2023
The crossing number of a graph G in a surface Σ, denoted by [Formula: see text], is the minimum number of pairwise intersections of edges in a drawing of G in Σ. Let k be an integer satisfying [Formula: see text], the generalized Petersen graph [Formula:
Jing Wang, Zuozheng Zhang
doaj   +1 more source

Exact Crossing Number Parameterized by Vertex Cover [PDF]

open access: yesInternational Symposium Graph Drawing and Network Visualization, 2019
We prove that the exact crossing number of a graph can be efficiently computed for simple graphs having bounded vertex cover. In more precise words, Crossing Number is in FPT when parameterized by the vertex cover size. This is a notable advance since we
Petr Hliněný, Abhisekh Sankaran
semanticscholar   +1 more source

Skewness and the crossing numbers of graphs

open access: yesAIMS Mathematics, 2023
The skewness of a graph $ G $, $ sk(G) $, is the smallest number of edges that need to be removed from $ G $ to make it planar. The crossing number of a graph $ G $, $ cr(G) $, is the minimum number of crossings over all possible drawings of $ G $. There
Zongpeng Ding
doaj   +1 more source

On the Decay of Crossing Numbers [PDF]

open access: yesJournal of Combinatorial Theory, Series B, 2007
The crossing number cr(G) of a graph G is the minimum number of crossings over all drawings of G in the plane. In 1993, Richter and Thomassen [RT93] conjectured that there is a constant c such that every graph G with crossing number k has an edge e such that cr(G- e) ≥ k - c√k.
Jacob Fox, Csaba D. Tóth
openaire   +3 more sources

Crossing lemma for the odd-crossing number

open access: yesComputational Geometry, 2023
A graph is $1$-planar, if it can be drawn in the plane such that there is at most one crossing on every edge. It is known, that $1$-planar graphs have at most $4n-8$ edges. We prove the following odd-even generalization. If a graph can be drawn in the plane such that every edge is crossed by at most one other edge {\em an odd number of times}, then it ...
Karl, János, Tóth, Géza
openaire   +3 more sources

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