Results 271 to 280 of about 307,259 (304)
Some of the next articles are maybe not open access.
Graphs and Combinatorics, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ku, Cheng Yeaw, Wong, Kok Bin
openaire +3 more sources
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ku, Cheng Yeaw, Wong, Kok Bin
openaire +3 more sources
Crossing Number and Weighted Crossing Number of Near-Planar Graphs
Algorithmica, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sergio Cabello, Bojan Mohar
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, Gasper Fijavz, Bojan Mohar
openaire +1 more source
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, Gasper Fijavz, Bojan Mohar
openaire +1 more source
On the parity of crossing numbers
Journal of Graph Theory, 1988AbstractFor an integer n ⩾ 1, a graph G has an n‐constant crossing number if, for any two good drawings ϕ and ϕ′ of G in the plane, μ(ϕ) ≡ μ(ϕ′) (mod n), where μ(ϕ) is the number of crossings in ϕ. We prove that, except for trivial cases, a graph G has n‐constant crossing number if and only if n = 2 and G is either Kp or Kq,r, where p, q, and r are odd.
Dan Archdeacon, R. Bruce Richter
openaire +2 more sources
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 +1 more source
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 +1 more source
The Crossing Number of Twisted Graphs
Graphs and Combinatorics, 2022The complete twisted graph \(T_n\) is a complete simple topological graph with vertices \(v_1, v_2, \dots, v_n\) such that two edges \(v_iv_j\) and \(v_pv_q\) cross if and only if ...
Bernardo M. Ábrego +4 more
openaire +2 more sources
Random Structures & Algorithms, 2008
AbstractThe biplanar crossing number cr2(G) of a graph G is min{cr(G1) + cr(G2)}, where cr is the planar crossing number. We show that cr2(G) ≤ (3/8)cr(G). Using this result recursively, we bound the thickness by Θ(G) ‐ 2 ≤ Kcr2(G)0.4057 log2n with some constant K.
Éva Czabarka +3 more
openaire +2 more sources
AbstractThe biplanar crossing number cr2(G) of a graph G is min{cr(G1) + cr(G2)}, where cr is the planar crossing number. We show that cr2(G) ≤ (3/8)cr(G). Using this result recursively, we bound the thickness by Θ(G) ‐ 2 ≤ Kcr2(G)0.4057 log2n with some constant K.
Éva Czabarka +3 more
openaire +2 more sources
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 ${\mbox{pcr}}G \geq c \frac{m^3}{n^2}$ .
Eyal Ackerman, Marcus Schaefer 0001
openaire +1 more source
On the crossing number of complete graphs
Proceedings of the eighteenth annual symposium on Computational geometry, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Oswin Aichholzer +2 more
openaire +1 more source
THE ADDITIVITY OF CROSSING NUMBERS
Journal of Knot Theory and Its Ramifications, 2004It 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