Geodesic
On a generalization of Meyniel's conjecture on the Cops and Robbers game
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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We consider a variant of the Cops and Robbers game where the robber can move $s$ edges at a time, and show that in this variant, the cop number of a connected graph on $n$ vertices can be as large as $\Omega(n^\frac{s}{s+1})$. This improves the $\Omega(n^{\frac{s-3}{s-2}})$ lower bound of Frieze et al., and extends the result of the second author, which establishes the above bound for $s=2,4$.
DOI : 10.37236/506
Classification : 05C57, 91A24, 91A43 
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     author = {Noga Alon and Abbas Mehrabian},
     title = {On a generalization of {Meyniel's} conjecture on the {Cops} and {Robbers} game},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/506},
     zbl = {1205.05159},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/506/}
}
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Noga Alon; Abbas Mehrabian. On a generalization of Meyniel's conjecture on the Cops and Robbers game. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/506

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