A coloring of the vertices of a graph $G$ is said to be distinguishing provided that no nontrivial automorphism of $G$ preserves all of the vertex colors. The distinguishing number of $G$, denoted $D(G)$, is the minimum number of colors in a distinguishing coloring of $G$. The distinguishing number, first introduced by Albertson and Collins in 1996, has been widely studied and a number of interesting results exist throughout the literature. In this paper, the notion of distinguishing colorings is extended to that of list-distinguishing colorings. Given a family $L=\{L(v)\}_{v\in V(G)}$ of lists assigning available colors to the vertices of $G$, we say that $G$ is $L$-distinguishable if there is a distinguishing coloring $f$ of $G$ such that $f(v)\in L(v)$ for all $v$. The list-distinguishing number of $G$, $D_{\ell}(G)$, is the minimum integer $k$ such that $G$ is $L$-distinguishable for any assignment $L$ of lists with $|L(v)|=k$ for all $v$. Here, we determine the list-distinguishing number for several families of graphs and highlight a number of distinctions between the problems of distinguishing and list-distinguishing a graph.

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An intervalp-graph is the intersection graph of a collection of intervals which have been colored withpdifferent colors with edges corresponding to nonempty intersection of intervals from different color classes. We characterize the class of 2-trees which are interval 3-graphs via a list of three graphs and three infinite families of forbidden induced subgraphs.

Increasing the inclusion of underrepresented individuals in coding is an intractable problem, with a variety of initiatives trying to improve the situation. Many of these initiatives involve STEAM education, which combines the arts with traditional STEM disciplines. Evidence is emerging that this approach is making headway on this complex problem. We present one such initiative, iLumiDance Coding, which attempts to pique the interest and increase confidence of students in coding, by combining it with a fun and physical activity: dance. The connections between dance and coding, while not immediately obvious, are authentic, and we hypothesize that this approach will increase student comfort level with coding. We used student surveys of attitudes toward coding and a variety of statistical approaches to analyze our initiative. Each analysis showed a positive effect on student comfort level with coding. These results are useful for both educators and researchers since they contribute to a deeper understanding of how to increase interest in coding, which we hope will lead to an increase in representation.

An interval k-graph is the intersection graph of a family I of intervals of the real line partitioned into at most k classes with vertices adjacent if and only if their corresponding intervals intersect and belong to different classes. In this paper we discuss the interval k-graphs that are the incomparability graphs of orders; i.e., cocomparability interval k-graphs or interval k-orders. Interval 2-orders have been characterized in many ways, but we show that analogous characterizations do not carry over to interval k-orders, for k > 2. We describe the structure of interval k-orders, for any k, characterize the interval 3-orders (cocomparability interval 3-graphs) via one forbidden suborder (subgraph), and state a conjecture for interval k-orders (any k) that would characterize them via two forbidden suborders.