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The paper gives an accurate description of the qualitative structure of anadmissible BV solution to a strictly hyperbolic, piecewise genuinely nonlinearsystem of conservation laws. We prove that there are a countable set $\Theta$which contains all interaction points and a family of countably many Lipschitzcurves $\T$ such that outside $\T\cup \Theta$ $u$ is continuous, and along thecurves in $\T$, u has left and right limit except for points in $\Theta$. Thisextends the corresponding structural result in \cite{BL,Liu1} for admissiblesolutions.  The proof is based on approximate wave-front tracking solutions and a properselection of discontinuity curves in the approximate solutions, which convergeto curves covering the discontinuities in the exact solution $u$.

Global structure of admissible BV solutions to piecewise genuinely nonlinear, strictly hyperbolic conservation laws in one space dimension