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PreprintCC BY-NC-ND 4.0arXiv

Fast robbers on abelian Cayley graphs and digraphs

  • Arindam Biswas
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Abstract

We study the fast-robber version of the Cops and Robbers game on finite strongly connected abelian Cayley digraphs, including undirected Cayley graphs as the symmetric case. For bounded out-degree D, we show that c1,∞(Γ)=OD(n1−1/D); in the undirected case with D≥2, this improves to the optimal exponent 1−1/(⌊ D/2⌋). We also establish the degree-independent bound c1,∞(Γ)=O ((n(loglog n)2)/(log n)). These estimates follow from an optimized character-theoretic cyclic sweep over subgroup quotients.

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Cite

BibTeXRIS
BibTeX
@misc{biswas2026fast,
  title = {{Fast robbers on abelian Cayley graphs and digraphs}},
  author = {Arindam Biswas},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.30474},
  eprint = {2608.30474},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30474},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Fast robbers on abelian Cayley graphs and digraphs
AU  - Arindam Biswas
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2608.30474
UR  - https://arxiv.org/abs/2608.30474
AB  - We study the fast-robber version of the Cops and Robbers game on finite strongly connected abelian Cayley digraphs, including undirected Cayley graphs as the symmetric case. For bounded out-degree D, we show that c_1,∞(Γ)=O_D(n^1−1/D); in the undirected case with D≥2, this improves to the optimal exponent 1−1/(⌊ D/2⌋). We also establish the degree-independent bound c_1,∞(Γ)=O ((n(loglog n)^2)/(log n)). These estimates follow from an optimized character-theoretic cyclic sweep over subgroup quotients.
ER  -