Digraph decompositions and Eulerian systems
SIAM Journal on Algebraic and Discrete Methods
Journal of Combinatorial Theory Series B
Algorithmic complexity in coding theory and the minimum distance problem
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Approximating rank-width and clique-width quickly
ACM Transactions on Algorithms (TALG)
A deterministic reduction for the gap minimum distance problem: [extended abstract]
Proceedings of the forty-first annual ACM symposium on Theory of computing
Universal Blind Quantum Computation
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Resources required for preparing graph states
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Hardness of approximating the minimum distance of a linear code
IEEE Transactions on Information Theory
Some randomized code constructions from group actions
IEEE Transactions on Information Theory
Parameterized complexity of weak odd domination problems
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
Pseudo-telepathy games and genuine ns k-way nonlocality using graph states
Quantum Information & Computation
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The local minimum degree of a graph is the minimum degree reached by means of a series of local complementations. In this paper, we investigate on this quantity which plays an important role in quantum computation and quantum error correcting codes. First, we show that the local minimum degree of the Paley graph of order p is greater than $\sqrt{p} - \frac{3}{2}$, which is, up to our knowledge, the highest known bound on an explicit family of graphs. Probabilistic methods allows us to derive the existence of an infinite number of graphs whose local minimum degree is linear in their order with constant 0.189 for graphs in general and 0.110 for bipartite graphs. As regards the computational complexity of the decision problem associated with the local minimum degree, we show that it is NP-complete and that there exists no l-approximation algorithm for this problem for any constant l unless P=NP.