Ekim, Tina Ries, Bernard de Werra, Dominique 2010 The split-coloring problem is a generalized vertex coloring problem where we partition the vertices into a minimum number of split graphs. In this paper, we study some notions which are extensively studied for the usual vertex coloring and the cocoloring problem from the point of view of split-coloring, such as criticality and the uniqueness of the minimum split-coloring. We discuss some properties of split-critical and uniquely split-colorable graphs. We describe constructions of such graphs with some additional properties. We also study the effect of the addition and the removal of some edge sets on the value of the split-chromatic number. All these results are compared with their cochromatic counterparts. We conclude with several research directions on the topic. application/pdf https://folia.unifr.ch/global/documents/308032 https://folia.unifr.ch/documents/308032/files/split-critical_0.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.46298/dmtcs.484 info:eu-repo/semantics/openAccess License undefined Discrete Mathematics and Theoretical Computer Science. - 2010, vol. 12, no. 5, p. 1-24 Theoretical Computer Science Discrete Mathematics and Combinatorics info:eu-repo/classification/udc/004 Split-critical and uniquely split-colorable graphs http://purl.org/coar/resource_type/c_6501