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Unconditional Lower Bounds for Degree Fault Tolerant Spanners

Authors Greg Bodwin , Aleksey Lopez

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LIPIcs.ESA.2026.31.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Paths and connectivity problems
  • Mathematics of computing → Extremal graph theory
  • Mathematics of computing → Graph algorithms
Keywords
  • Spanners
  • Fault Tolerance
  • Girth Conjecture
  • Wenger Graphs

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Abstract

We study multiplicative graph spanners in the f-degree fault tolerant (f-DFT) model, in which the spanner must approximately preserve distances even after any subset of edges of maximum degree f temporarily "fails" and is removed from the graph. We prove that there are n-node lower bound graphs for which any f-DFT (2k-1)-stretch spanner H must have size |E(H)| ≥ Ω(f^{1-1/k} n^{1+1/k}) . This matches a lower bound that was previously only known to hold conditionally, under the 1963 girth conjecture of Erdős. It also matches the current upper bounds, up to a factor of exp(k). Our proof is an analysis of the so-called Wenger graphs (J. Comb. Theory 1991), via their recent reinterpretation by Szabó and by Conlon (Am. Math. Monthly 2021).

Cite As Get BibTex

Greg Bodwin and Aleksey Lopez. Unconditional Lower Bounds for Degree Fault Tolerant Spanners. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 31:1-31:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.31

Author Details

Greg Bodwin
  • Department of EECS, University of Michigan, Ann Arbor, MI, USA
Aleksey Lopez
  • Department of EECS, University of Michigan, Ann Arbor, MI, USA

Funding

  • Bodwin, Greg: Supported in part by NSF:AF 2153680.

References

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