Graph pebbling is a network optimization model for transporting discrete resources that are consumed in transit: the movement of 2 pebbles across an edge consumes one of the pebbles. The pebbling number of a graph is the fewest number of pebbles t so that, from any initial configuration of t pebbles on its vertices, one can place a pebble on any given target vertex via such pebbling steps. It is known that deciding whether a given configuration on a particular graph can reach a specified target is NP-complete, even for diameter 2 graphs, and that deciding whether the pebbling number has a prescribed upper bound is Π[P over 2]-complete. On the other hand, for many families of graphs there are formulas or polynomial algorithms for computing pebbling numbers; for example, complete graphs, products of paths (including cubes), trees, cycles, diameter 2 graphs, and more. Moreover, graphs having minimum pebbling number are called Class 0, and many authors have studied which graphs are Class 0 and what graph properties guarantee it, with no characterization in sight. In this paper we investigate an important family of diameter 3 chordal graphs called split graphs; graphs whose vertex set can be partitioned into a clique and an independent set. We provide a formula for the pebbling number of a split graph, along with an algorithm for calculating it that runs in O(n[superscript β]) time, where β = 2ω/(ω + 1) [= over ∼] 1.41 and ω [= over ∼] 2.376 is the exponent of matrix multiplication. Furthermore we determine that all split graphs with minimum degree at least 3 are Class 0.

Objectives: To determine the off-shift sleep strategies of bi-ethnic night-shift nurses, the relationship between these sleep strategies and adaptation to shift work, and identify the participant-level characteristics associated with a given sleep strategy.

Methods: African-American and non-Hispanic White female, night-shift nurses from an academic hospital were recruited to complete a survey on sleep–wake patterns (n = 213). Participants completed the standard shiftwork index and the biological clocks questionnaire to determine sleep strategies and adaptation to night-shift work. In addition, chronotype was determined quantitatively with a modified version of the Munich ChronoType Questionnaire. Most participants worked ~3 consecutive 12-h night-shifts followed by several days off.

Results: Five sleep strategies used on days off were identified: (a) night stay, (b) nap proxy, (c) switch sleeper, (d) no sleep, and (e) incomplete switcher. Nap proxy and no sleep types were associated with poorer adaptation to night-shift work. The switch sleeper and incomplete switcher types were identified as more adaptive strategies that were associated with less sleep disturbance, a later chronotype, and less cardiovascular problems.

Conclusion: Behavioral sleep strategies are related to adaptation to a typical night-shift schedule among hospital nurses. Nurses are crucial to the safety and well-being of their patients. Therefore, adoption of more adaptive sleep strategies may reduce sleep/wake dysregulation in this population, and improve cardiovascular outcomes.