4 citations · 4 across the 2 of their papers we have counts for
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The principal Erdős--Gallai differences of a degree sequence
Michael D. Barrus
The Erdős--Gallai criteria for recognizing degree sequences of simple graphs involve a system of inequalities. Given a fixed degree sequence, we consider the list of differences of…
Graphs with few trivial characteristic ideals
Carlos A. Alfaro, Michael D. Barrus, John Sinkovic +1
We give a characterization of the graphs with at most three trivial characteristic ideals. This implies the complete characterization of the regular graphs whose critical groups ha…
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…
Classes of critical graphs for tree-depth
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…