Reliability polynomial roots of simple graphs are dense in the unit disk, with real roots dense in [-1,0] union {1}.
Real Reliability Roots of Simple Graphs are Dense
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We prove that the closure of the real roots of all-terminal reliability polynomials is exactly $[-1,0] \cup \{1\}$, resolving a conjecture of Brown and McMullin and refining the corresponding density result for multigraphs due to Brown and Colbourn. The crux of the proof is demonstrating that real reliability roots of edge-substitution graphs $G[H]$, where $G$ ranges over connected multigraphs and $H$ ranges over complete graphs missing an edge, are dense.
fields
math.CO 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
Density of reliability roots of simple graphs in the unit disk
Reliability polynomial roots of simple graphs are dense in the unit disk, with real roots dense in [-1,0] union {1}.