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Split-critical and uniquely split-colorable graphs

Ekim, Tina ; Ries, Bernard ; de Werra, Dominique

In: Discrete Mathematics and Theoretical Computer Science, 2010, vol. 12, no. 5, p. 1-24

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...