On a Crossing Number Result of Richter and Thomassen
نویسندگان
چکیده
منابع مشابه
Beyond the Richter-Thomassen Conjecture
If two closed Jordan curves in the plane have precisely one point in common, then it is called a touching point. All other intersection points are called crossing points. The main result of this paper is a Crossing Lemma for closed curves: In any family of n pairwise intersecting simple closed curves in the plane, no three of which pass through the same point, the number of crossing points exce...
متن کاملOn the Richter-Thomassen Conjecture about Pairwise Intersecting Closed Curves
A long standing conjecture of Richter and Thomassen states that the total number of intersection points between any n simple closed Jordan curves in the plane, so that any pair of them intersect and no three curves pass through the same point, is at least (1− o(1))n. We confirm the above conjecture in several important cases, including the case (1) when all curves are convex, and (2) when the f...
متن کاملCrossing number, pair-crossing number, and expansion
The crossing number crðGÞ of a graph G is the minimum possible number of edge crossings in a drawing of G in the plane, while the pair-crossing number pcrðGÞ is the smallest number of pairs of edges that cross in a drawing of G in the plane. While crðGÞXpcrðGÞ holds trivially, it is not known whether a strict inequality can ever occur (this question was raised by Mohar and Pach and Tóth). We ai...
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In 1989, Thomassen asked whether there is an integer-valued function f(k) such that every f(k)-connected graph admits a spanning, bipartite k-connected subgraph. In this paper we take a first, humble approach, showing the conjecture is true up to a log n factor.
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: 2000
ISSN: 0095-8956
DOI: 10.1006/jctb.1999.1943