Add to ORKGAbstract. We prove that on a punctured oriented surface with Euler characteristic χ < 0, the maximal cardinality of a set of essential simple arcs that are pairwise non-homotopic and intersecting at most once is 2|χ|(|χ|+1). This gives a cubic estimate in |χ | for a set of curves pairwise intersecting at most once on a closed surface. We also give polynomial estimates in |χ | for sets of arcs and curves pairwise intersecting a uniformly bounded number of times. Finally, we prove that on a punctured sphere the maximal cardinality of a set of arcs starting and ending at specified punctures and pairwise intersecting at most once is 12 |χ|(|χ | + 1).
59 pages, 33 figures, revised version accepted to Journal of the ACM. The time complexity for testin...
59 pages, 33 figures, revised version accepted to Journal of the ACM. The time complexity for testin...
AbstractIt is proved that for each compact (bordered) surfaceΣand each integerkthere is a constantNw...
We consider a punctured sphere of negative Euler characteristic, and a collection of essential, simp...
International audienceWe study filling sets of simple closed curves on punctured surfaces. In partic...
Let P be a set of n points in the plane and let C be a family of simple closed curves in the plane e...
Abstract. We show that the asymptotic growth rate for the minimal cardinality of a set of simple clo...
Consider a set of simple closed curves on a surface of genus g which fill the surface and which pair...
A long standing conjecture of Richter and Thomassen states that the total number of intersection poi...
AbstractWe show that the asymptotic growth rate for the minimal cardinality of a set of simple close...
A long-standing conjecture of Richter and Thomassen states that the total number of intersection poi...
\u3cp\u3eGiven a set of planar curves (Jordan arcs), each pair of which meets — either crosses or to...
The sporadic complete $12$-arc in $\mathrm{PG}(2,13)$ contains eight points from a conic. In $\mathr...
The sporadic complete $12$-arc in $\mathrm{PG}(2,13)$ contains eight points from a conic. In $\mathr...
The sporadic complete $12$-arc in $\mathrm{PG}(2,13)$ contains eight points from a conic. In $\mathr...
59 pages, 33 figures, revised version accepted to Journal of the ACM. The time complexity for testin...
59 pages, 33 figures, revised version accepted to Journal of the ACM. The time complexity for testin...
AbstractIt is proved that for each compact (bordered) surfaceΣand each integerkthere is a constantNw...
We consider a punctured sphere of negative Euler characteristic, and a collection of essential, simp...
International audienceWe study filling sets of simple closed curves on punctured surfaces. In partic...
Let P be a set of n points in the plane and let C be a family of simple closed curves in the plane e...
Abstract. We show that the asymptotic growth rate for the minimal cardinality of a set of simple clo...
Consider a set of simple closed curves on a surface of genus g which fill the surface and which pair...
A long standing conjecture of Richter and Thomassen states that the total number of intersection poi...
AbstractWe show that the asymptotic growth rate for the minimal cardinality of a set of simple close...
A long-standing conjecture of Richter and Thomassen states that the total number of intersection poi...
\u3cp\u3eGiven a set of planar curves (Jordan arcs), each pair of which meets — either crosses or to...
The sporadic complete $12$-arc in $\mathrm{PG}(2,13)$ contains eight points from a conic. In $\mathr...
The sporadic complete $12$-arc in $\mathrm{PG}(2,13)$ contains eight points from a conic. In $\mathr...
The sporadic complete $12$-arc in $\mathrm{PG}(2,13)$ contains eight points from a conic. In $\mathr...
59 pages, 33 figures, revised version accepted to Journal of the ACM. The time complexity for testin...
59 pages, 33 figures, revised version accepted to Journal of the ACM. The time complexity for testin...
AbstractIt is proved that for each compact (bordered) surfaceΣand each integerkthere is a constantNw...