Improvement on the Crossing Number of Crossing-Critical Graphs
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 .
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2020 ◽
Vol 29
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pp. 2050022
1997 ◽
Vol 6
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pp. 353-358
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2000 ◽
Vol 10
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pp. 73-78
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2015 ◽
Vol 24
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pp. 1550006
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