On the crossing number of K13
نویسندگان
چکیده
منابع مشابه
On the Maximum Crossing Number
Research about crossings is typically about minimization. In this paper, we consider maximizing the number of crossings over all possible ways to draw a given graph in the plane. Alpert et al. [1] conjectured that any graph has a convex straight-line drawing, e.g., a drawing with vertices in convex position, that maximizes the number of edge crossings. We disprove this conjecture by constructin...
متن کاملOn the Degenerate Crossing Number
The degenerate crossing number cr∗(G) of a graph G is the minimum number of crossing points of edges in any drawing of G as a simple topological graph in the plane. This notion was introduced by Pach and Tóth who showed that for a graph G with n vertices and e ≥ 4n edges cr∗(G) = Ω(e/n). In this paper we completely resolve the main open question about degenerate crossing numbers and show that c...
متن کاملOn the Pseudolinear Crossing Number
4 A drawing of a graph is pseudolinear if there is a pseudoline arrangement such that 5 each pseudoline contains exactly one edge of the drawing. The pseudolinear crossing 6 number c̃r(G) of a graph G is the minimum number of pairwise crossings of edges in 7 a pseudolinear drawing of G. We establish several facts on the pseudolinear crossing 8 number, including its computational complexity and i...
متن کاملOn the Pair-Crossing Number
By a drawing of a graph G, we mean a drawing in the plane such that vertices are represented by distinct points and edges by arcs. The crossing number cr(G) of a graph G is the minimum possible number of crossings in a drawing of G. The pair-crossing number pair-cr(G) of G is the minimum possible number of (unordered) crossing pairs in a drawing of G. Clearly, pair-cr(G) ≤ cr(G) holds for any g...
متن کاملOn Crossing Number of Knots
The aim of this paper is to endow a monoid structure on the set S of all oriented knots(links) under the operation ⊎ , called addition of knots. Moreover, we prove that there exists a homomorphism of monoids between (Sd, ⊎ ) to (N, +), where Sd is a subset of S with an extra condition and N is the monoid of non negative integers under usual addition.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2015
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2015.06.002