Abstract
A (homogeneous) d-interval is a union of d closed intervals in the line. Let H be a finite collection of d-intervals. The transversal number τ (H) of H is the minimum number of points that intersect every member of H. The matching number v(H) of H is the maximum number of pairwise disjoint members of H. Gyárfás and Lehel [3] proved that τ ≤ O(vd!) and Kaiser [4] proved that τ ≤ O(d2v). His proof is topological, applies the Borsuk-Ulam theorem, and extends and simplifies a result of Tardos [5]. Here we give a very short, elementary proof of a similar estimate, using the method of [2].
Original language | English (US) |
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Pages (from-to) | 333-334 |
Number of pages | 2 |
Journal | Discrete and Computational Geometry |
Volume | 19 |
Issue number | 3 |
DOIs | |
State | Published - Apr 1998 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics