158 lines
4.9 KiB
BibTeX
158 lines
4.9 KiB
BibTeX
% ── Cops-and-robbers background ─────────────────────────────────────────────
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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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number = {1},
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year = {1984},
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pages = {1--12},
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}
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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{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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}
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@article{PralatWormaldRegular,
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author = {Pra{\l}at, P. and Wormald, N.},
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title = {{Meyniel}'s conjecture holds for random $d$-regular graphs},
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journal = {Random Structures \& Algorithms},
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volume = {55},
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number = {3},
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year = {2019},
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pages = {719--741},
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}
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@misc{NeuwirthBranchCapture,
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author = {Neuwirth, Levi},
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title = {Branch-tube persistence and static coverage in tree-ball geometry},
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note = {Preprint},
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year = {2026},
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url = {https://levineuwirth.org/essays/branch-based-local-capture-in-tree-balls/index.html},
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}
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% ── Random-regular / configuration-model background ────────────────────────
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@incollection{Wormald,
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author = {Wormald, N. C.},
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title = {Models of random regular graphs},
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booktitle = {Surveys in Combinatorics, 1999},
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series = {London Mathematical Society Lecture Note Series},
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volume = {267},
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publisher = {Cambridge University Press},
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year = {1999},
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pages = {239--298},
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}
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@article{Janson,
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author = {Janson, S.},
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title = {The probability that a random multigraph is simple},
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journal = {Combinatorics, Probability and Computing},
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volume = {18},
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year = {2009},
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pages = {205--225},
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}
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% ── Domination in regular / random graphs ───────────────────────────────────
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@book{CohenHonkalaLitsynLobstein,
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author = {Cohen, G. and Honkala, I. and Litsyn, S. and Lobstein, A.},
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title = {Covering Codes},
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series = {North-Holland Mathematical Library},
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volume = {54},
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publisher = {Elsevier},
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year = {1997},
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}
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@article{Duckworth,
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author = {Duckworth, W.},
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title = {Randomized greedy algorithms for finding small $k$-dominating sets of regular graphs},
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journal = {Random Structures \& Algorithms},
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volume = {27},
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year = {2005},
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pages = {401--412},
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}
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@article{DuckworthWormald,
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author = {Duckworth, W. and Wormald, N. C.},
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title = {On the independent domination number of random regular graphs},
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journal = {Combinatorics, Probability and Computing},
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volume = {15},
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year = {2006},
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pages = {513--522},
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}
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@article{CutlerRadcliffe,
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author = {Cutler, J. and Radcliffe, A. J.},
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title = {Counting dominating sets and related structures in graphs},
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journal = {Discrete Mathematics},
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volume = {339},
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year = {2016},
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pages = {1593--1599},
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}
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@article{GlebovLiebenauSzabo,
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author = {Glebov, R. and Liebenau, A. and Szab{\'o}, T.},
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title = {On the concentration of the domination number of the random graph},
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journal = {SIAM Journal on Discrete Mathematics},
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volume = {29},
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year = {2015},
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pages = {1186--1206},
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}
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% ── Statistical-mechanics / message-passing antecedents ─────────────────────
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@article{ZhaoHabibullaZhou,
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author = {Zhao, J.-H. and Habibulla, Y. and Zhou, H.-J.},
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title = {Statistical mechanics of the minimum dominating set problem},
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journal = {Journal of Statistical Physics},
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volume = {159},
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year = {2015},
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pages = {1154--1174},
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}
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@misc{HabibullaQin,
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author = {Habibulla, Y. and Qin, S.-m.},
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title = {Two-distance minimal dominating set problem studied by statistical mechanics and simulated annealing},
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howpublished = {arXiv:1910.07933},
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year = {2019},
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}
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% ── Variational-analysis background ─────────────────────────────────────────
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@book{RockafellarWets,
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author = {Rockafellar, R. T. and Wets, R. J.-B.},
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title = {Variational Analysis},
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series = {Grundlehren der mathematischen Wissenschaften},
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volume = {317},
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publisher = {Springer},
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year = {1998},
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}
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