Abstract
AbstractThe crossing number of a graph G is the minimum number of edge crossings over all drawings of G in the plane. A graph G is k-crossing-critical if its crossing number is at least k, but if we remove any edge of G, its crossing number drops below k. There are examples of k-crossing-critical graphs that do not have drawings with exactly k crossings. Richter and Thomassen proved in 1993 that if G is k-crossing-critical, then its crossing number is at most $$2.5\, k+16$$
2.5
k
+
16
. We improve this bound to $$2k+8\sqrt{k}+47$$
2
k
+
8
k
+
47
.
Funder
Hungarian Ministry for Innovation and Technology
Hungarian Scientific Research Fund
Nemzeti Kutatási Fejlesztési és Innovációs Hivatal
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Theoretical Computer Science
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