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math.CO2016
Weakly threshold graphs
Michael D. Barrus
We define a weakly threshold sequence to be a degree sequence of a graph having the property that $\sum_{i \leq k} d_i \geq k(k-1)+\sum_{i > k} \min\{k,d_i\} -…
math.CO2016
Minimal obstructions for tree-depth: A non-1-unique example
Michael D. Barrus, John Sinkovic
A k-ranking of a graph G is a labeling of the vertices of G with values from 1,...,k such that any path joining two vertices with the same label contains a vertex having a higher l…