Linear properties of Banach spaces and low distortion embeddings of   metric graphs
  We characterize non-reflexive Banach spaces by a low-distortion (resp. isometric) embeddability of a certain metric graph up to a renorming. Also we study non-linear sufficient conditions for $\ell_1^n$ being $(1+\varepsilon)$-isomorphic to a subspace of a Banach space $X$. 
Antonin Prochazka
math.FA