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Let X, Y be asymmetric normed spaces and Lc(X, Y) the convex cone of all linear continuous operators from X to Y. It is known that in general, Lc(X, Y) is not a vector space. The aim of this note is to prove, using the Baire category theorem, that if Lc(X, Y) is a vector space for some asymmetric normed space Y , then X is isomorphic to its associated normed space (the converse is true for every asymmetric normed space Y and is easy to establish). For this, we introduce an index of symmetry of the space X denoted c(X) $\in$ [0, 1] and we give the link between the index c(X) and the fact that Lc(X, Y) is in turn an asymmetric normed space for every asymmetric normed space Y. Our study leads to a topological classification of asymmetric normed spaces.

We introduce a dynamic version of the graph coloring problem and prove its fixed-parameter tractability with respect to the edit-parameter. This is used to present a {\em turbo-charged} heuristic for the problem that works by combining the turbo-charging technique with other standard heuristic tools, including greedy coloring. The recently introduced turbo-charging idea is further enhanced in this paper by introducing a dynamic version of the so called {\em moment of regret} and {\em rollback points}. Experiments comparing our turbo-charging algorithm to other heuristics demonstrate its effectiveness. Our algorithm often produced results that were either exact or better than all the other available heuristics.