Flips in Graphs
Tom Bohman, Andrzej Dudek, Alan Frieze, and Oleg Pikhurko

TL;DR
This paper investigates a graph parameter related to quantum-error-correcting codes, providing asymptotic estimates for random graphs and bounds on the maximum value of this parameter for graphs of size n.
Contribution
It introduces and analyzes a new graph parameter, offering tight asymptotic estimates for random graphs and bounds on its maximum over all graphs of a given size.
Findings
Asymptotically tight estimates of f(G) for G_{n,p} when p is constant.
Upper bound of (0.382+o(1))n for the maximum of f(G) over graphs with n vertices.
Connections to quantum-error-correcting codes and combinatorial graph properties.
Abstract
We study a problem motivated by a question related to quantum-error-correcting codes. Combinatorially, it involves the following graph parameter: where is the vertex set of and is the number of neighbors of in . We give asymptotically tight estimates of for the random graph when is constant. Also, if then we show that .
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Coding theory and cryptography · Quantum-Dot Cellular Automata
