scholarly journals The crossing number of hexagonal graph H_{3,N} in the projective plane

2019 ◽  
Author(s):  
Junliang Cai ◽  
YuanQiu Huang ◽  
Shengxiang Lv ◽  
Jing Wang
Keyword(s):  
Projective Plane ◽  
Crossing Number ◽  
Hexagonal Graph

The projective plane crossing number ofC3 ×Cn

1993 ◽  
Vol 17 (6) ◽  
pp. 683-693
Author(s):  
Adrian Riskin
Keyword(s):  
Projective Plane ◽  
Crossing Number

scholarly journals The Crossing Number of a Projective Graph is Quadratic in the Face–Width

10.37236/770 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
I. Gitler ◽  
P. Hliněný ◽  
J. Leaños ◽  
G. Salazar
Keyword(s):  
Approximation Algorithm ◽  
Projective Plane ◽  
Crossing Number ◽  
Orientable Surface ◽  
Constant Factor ◽  
Bounded Degree ◽  
Face Width ◽  
Projective Graph ◽  
The Face ◽  
Large Face

We show that for each integer $g\geq0$ there is a constant $c_g > 0$ such that every graph that embeds in the projective plane with sufficiently large face–width $r$ has crossing number at least $c_g r^2$ in the orientable surface $\Sigma_g$ of genus $g$. As a corollary, we give a polynomial time constant factor approximation algorithm for the crossing number of projective graphs with bounded degree.

scholarly journals The crossing number of the hexagonal graph H_{3,n}

2019 ◽  
Vol 39 (2) ◽  
pp. 547 ◽  
Author(s):  
YuanQiu Huang ◽  
ZhangDong Ouyang ◽  
Jing Wang
Keyword(s):  
Crossing Number ◽  
Hexagonal Graph

Gilles Deleuze's Luminous Philosophy

2020 ◽  
Author(s):  
Hanjo Berressem
Keyword(s):  
Projective Plane ◽  
Visual Arts ◽  
Whole Body ◽  
Literary Studies ◽  
Chronological Order ◽  
Real Projective Plane ◽  
Cinema Studies ◽  
The Real

Providing a comprehensive reading of Deleuzian philosophy, Gilles Deleuze’s Luminous Philosophy argues that this philosophy’s most consistent conceptual spine and figure of thought is its inherent luminism. When Deleuze notes in Cinema 1 that ‘the plane of immanence is entirely made up of light’, he ties this philosophical luminism directly to the notion of the complementarity of the photon in its aspects of both particle and wave. Engaging, in chronological order, the whole body and range of Deleuze’s and Deleuze and Guattari’s writing, the book traces the ‘line of light’ that runs through Deleuze’s work, and it considers the implications of Deleuze’s luminism for the fields of literary studies, historical studies, the visual arts and cinema studies. It contours Deleuze’s luminism both against recent studies that promote a ‘dark Deleuze’ and against the prevalent view that Deleuzian philosophy is a philosophy of difference. Instead, it argues, it is a philosophy of the complementarity of difference and diversity, considered as two reciprocally determining fields that are, in Deleuze’s view, formally distinct but ontologically one. The book, which is the companion volume toFélix Guattari’s Schizoanalytic Ecology, argues that the ‘real projective plane’ is the ‘surface of thought’ of Deleuze’s philosophical luminism.

On the Crossing Number of $K_{m,n}$

10.37236/1748 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Nagi H. Nahas
Keyword(s):  
Lower Bound ◽  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Crossing Number

The best lower bound known on the crossing number of the complete bipartite graph is : $$cr(K_{m,n}) \geq (1/5)(m)(m-1)\lfloor n/2 \rfloor \lfloor(n-1)/2\rfloor$$ In this paper we prove that: $$cr(K_{m,n}) \geq (1/5)m(m-1)\lfloor n/2 \rfloor \lfloor (n-1)/2 \rfloor + 9.9 \times 10^{-6} m^2n^2$$ for sufficiently large $m$ and $n$.

THE CYLINDRICAL CROSSING NUMBER OF ZERO DIVISOR GRAPHS

2020 ◽  
Vol 9 (8) ◽  
pp. 5901-5908
Author(s):  
M. Sagaya Nathan ◽  
J. Ravi Sankar
Keyword(s):  
Zero Divisor ◽  
Crossing Number

scholarly journals Join Products K2,3 + Cn

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 925
Author(s):  
Michal Staš
Keyword(s):  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Crossing Number ◽  
Arithmetic Means ◽  
Minimum Number ◽  
Edge Crossings

The crossing number cr ( G ) of a graph G is the minimum number of edge crossings over all drawings of G in the plane. The main goal of the paper is to state the crossing number of the join product K 2 , 3 + C n for the complete bipartite graph K 2 , 3 , where C n is the cycle on n vertices. In the proofs, the idea of a minimum number of crossings between two distinct configurations in the various forms of arithmetic means will be extended. Finally, adding one more edge to the graph K 2 , 3 , we also offer the crossing number of the join product of one other graph with the cycle C n .

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