Geodesic
On the crossing number of \(K_{m,n}\)
The electronic journal of combinatorics, Tome 10 (2003)

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Zbl
The best lower bound known on the crossing number of the complete bipartite graph is : $$cr(K_{m,n}) \geq (1/5)(m)(m-1)\lfloor n/2 \rfloor \lfloor(n-1)/2\rfloor$$ In this paper we prove that: $$cr(K_{m,n}) \geq (1/5)m(m-1)\lfloor n/2 \rfloor \lfloor (n-1)/2 \rfloor + 9.9 \times 10^{-6} m^2n^2$$ for sufficiently large $m$ and $n$.
DOI : 10.37236/1748
Classification : 05C10, 05C35 
Nagi H. Nahas. On the crossing number of \(K_{m,n}\). The electronic journal of combinatorics, Tome 10 (2003). doi: 10.37236/1748
@article{10_37236_1748,
     author = {Nagi H. Nahas},
     title = {On the crossing number of {\(K_{m,n}\)}},
     journal = {The electronic journal of combinatorics},
     year = {2003},
     volume = {10},
     doi = {10.37236/1748},
     zbl = {1023.05039},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1748/}
}
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