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The article focuses on Rutgers Center for Operations Research (RUTCOR) director Peter L. Hammer and his contributions to several areas of mathematical research including Boolean models, combination optimization, and graph theory. Born in Timisoara, Romania on December 23, 1936, Hammer founded RUTCOR in 1983. Hammer's scientific contributions earned him awards such as the George Tzitzeica prize and the Euler Medal. Publications by Hammer are listed.

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. [ABSTRACT FROM AUTHOR]