127 lines
3.8 KiB
BibTeX
127 lines
3.8 KiB
BibTeX
% ── Foundational papers (cops-and-robbers) ──────────────────────────────────
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@article{AignerFromme,
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author = {Aigner, M. and Fromme, M.},
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title = {A game of cops and robbers},
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journal = {Discrete Applied Mathematics},
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volume = {8},
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year = {1984},
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pages = {1--12},
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}
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% ── Meyniel's conjecture: bounds and partial progress ───────────────────────
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@article{LuPeng,
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author = {Lu, L. and Peng, X.},
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title = {On {Meyniel}'s conjecture of the cop number},
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journal = {Journal of Graph Theory},
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volume = {71},
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number = {2},
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year = {2012},
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pages = {192--205},
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}
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@article{ScottSudakov,
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author = {Scott, A. and Sudakov, B.},
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title = {A bound for the cops and robbers problem},
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journal = {SIAM Journal on Discrete Mathematics},
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volume = {25},
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number = {3},
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year = {2011},
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pages = {1438--1442},
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}
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@article{BoseEsperetHodorJoretMicekRambaud,
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author = {Bose, P. and Esperet, L. and Hodor, J. and Joret, G. and Micek, P. and Rambaud, C.},
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title = {Cops and robber in graphs with bounded vertex cover number},
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journal = {arXiv:2602.07435},
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year = {2026},
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}
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@article{BradshawHosseiniMoharStacho,
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author = {Bradshaw, P. and Hosseini, S. A. and Mohar, B. and Stacho, L.},
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title = {On the cop number of graphs of high girth},
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journal = {Journal of Graph Theory},
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volume = {102},
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year = {2023},
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pages = {15--34},
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note = {arXiv:2005.10849},
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}
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@misc{Clow,
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author = {Clow, A.},
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title = {Expanders satisfy the weak {Meyniel} conjecture},
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year = {2023},
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note = {Withdrawn preprint, arXiv:2311.13792},
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}
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@article{HMG,
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author = {Hosseini, S. A. and Mohar, B. and {Gonzalez Hermosillo de la Maza}, S.},
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title = {{Meyniel}'s conjecture on graphs of bounded degree},
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journal = {Journal of Graph Theory},
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volume = {97},
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year = {2021},
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pages = {401--407},
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note = {arXiv:1912.06957},
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}
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@article{PralatWormald,
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author = {Pra{\l}at, P. and Wormald, N.},
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title = {{Meyniel}'s conjecture holds for random graphs},
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journal = {Random Structures \& Algorithms},
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volume = {48},
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number = {2},
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year = {2016},
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pages = {396--421},
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note = {arXiv:1301.2841},
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}
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% ── Expansion, isoperimetry, and product/replacement structures ────────────
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@article{BollobasKunLeader,
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author = {Bollob\'as, B. and Kun, G. and Leader, I.},
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title = {Cops and robbers in a random graph},
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journal = {Journal of Combinatorial Theory, Series B},
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volume = {103},
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year = {2013},
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pages = {226--236},
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}
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@article{BollobasLeader,
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author = {Bollob\'as, B. and Leader, I.},
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title = {An isoperimetric inequality on the discrete torus},
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journal = {SIAM Journal on Discrete Mathematics},
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volume = {3},
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year = {1990},
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pages = {32--37},
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}
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@article{ReingoldVadhanWigderson,
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author = {Reingold, O. and Vadhan, S. and Wigderson, A.},
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title = {Entropy waves, the zig-zag graph product, and new constant-degree expanders},
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journal = {Annals of Mathematics},
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volume = {155},
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year = {2002},
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pages = {157--187},
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}
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% ── Cop number on tori and products ─────────────────────────────────────────
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@article{Lehner,
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author = {Lehner, F.},
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title = {On the cop number of toroidal graphs},
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journal = {Journal of Combinatorial Theory, Series B},
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volume = {151},
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year = {2021},
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pages = {250--262},
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}
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@article{NeufeldNowakowski,
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author = {Neufeld, S. and Nowakowski, R.},
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title = {A game of cops and robbers played on products of graphs},
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journal = {Discrete Mathematics},
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volume = {186},
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year = {1998},
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pages = {253--268},
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}
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