### On the approximation of min split-coloring and min cocoloring.

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In this paper, we develop a divide-and-conquer approach, called block decomposition, to solve the minimum geodetic set problem. This provides us with a unified approach for all graphs admitting blocks for which the problem of finding a minimum geodetic set containing a given set of vertices (-extension problem) can be efficiently solved. Our method allows us to derive linear time algorithms for the minimum geodetic set problem in (a proper superclass of) block-cacti and monopolar chordal graphs....

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