Results 321 to 330 of about 10,813,555 (336)
Some of the next articles are maybe not open access.
Rectilinear Crossing Number of a Zero Divisor Graph
, 2013In this paper, we evaluate the rectilinear crossing number of Γ(Zn). We mainly focus on finding the rectilinear drawing of zero divisor complete graphs especially for p =7 , 11. Finally, we compare the rectilinear crossing number with the crossing number
M. Malathi +3 more
semanticscholar +1 more source
Journal of Graph Theory, 1978
AbstractResults giving the exact crossing number of an infinite family of graphs on some surface are very scarce. In this paper we show the following: for G = Qn × K4.4, cry(G)‐m(G) = 4m, for 0 ⩽ = m ⩽ 2n. A generalization is obtained, for certain repeated cartesian products of bipartite graphs. Nonorientable analogs are also developed.
Paul C. Kainen, Arthur T. White
openaire +2 more sources
AbstractResults giving the exact crossing number of an infinite family of graphs on some surface are very scarce. In this paper we show the following: for G = Qn × K4.4, cry(G)‐m(G) = 4m, for 0 ⩽ = m ⩽ 2n. A generalization is obtained, for certain repeated cartesian products of bipartite graphs. Nonorientable analogs are also developed.
Paul C. Kainen, Arthur T. White
openaire +2 more sources
THE ADDITIVITY OF CROSSING NUMBERS [PDF]
Journal of Knot Theory and Its Ramifications, 2004 It has long been conjectured that the crossing numbers of links are additive under the connected sum of links. This is a difficult problem in knot theory and has been open for more than 100 years. In fact, many questions of much weaker conditions are still open.
openaire +1 more source
SIAM Journal on Discrete Mathematics, 2006
The minor crossing number of a graph G is defined as the minimum crossing number of all graphs that contain G as a minor. Basic properties of this new invariant are presented. We study topological structure of graphs with bounded minor crossing number and obtain a new strong version of a lower bound based on the genus.
Drago Bokal, Bojan Mohar, Gasper Fijavz
openaire +2 more sources
The minor crossing number of a graph G is defined as the minimum crossing number of all graphs that contain G as a minor. Basic properties of this new invariant are presented. We study topological structure of graphs with bounded minor crossing number and obtain a new strong version of a lower bound based on the genus.
Drago Bokal, Bojan Mohar, Gasper Fijavz
openaire +2 more sources
Crossing Number is NP-Complete
, 1983In this paper we consider a problem related to questions of optimal circuit layout: Given a graph or network, how can we embed it in a planar surface so as to minimize the number of edge-crossings?
M. Garey, David S. Johnson
semanticscholar +1 more source
A Crossing Lemma for the Pair-Crossing Number
2014The pair-crossing number of a graph G, pcrG, is the minimum possible number of pairs of edges that cross each other possibly several times in a drawing of G. It is known that there is a constant ci¾?1/64 such that for every not too sparse graph G with n vertices and m edges ${\mbox{pcr}}G \geq c \frac{m^3}{n^2}$ .
Marcus Schaefer, Eyal Ackerman
openaire +2 more sources
On the biplanar crossing number
IEEE Transactions on Circuit Theory, 1971In the design of printed and integrated circuits it is desirable to minimize the number of jumpers and via-holes. Linear graph theory provides apparatus useful in the formal specification and solution of this problem. Prior work has concentrated on the drawing of graphs in a single plane.
openaire +2 more sources
On the Crossing Number of Kn without Computer Assistance
Journal of Graph Theory, 2016Dan McQuillan, R. Bruce Richter
semanticscholar +1 more source