14 citations · 64 across the 20 of their papers we have counts for
4 papers · 1 filter
On fractional realizations of graph degree sequences
Michael D. Barrus
We introduce fractional realizations of a graph degree sequence and a closely associated convex polytope. Simple graph realizations correspond to a subset of the vertices of this p…
Minimal forbidden sets for degree sequence characterizations
Michael D. Barrus, Stephen G. Hartke
Given a set of graphs, a graph is -free if does not contain any member of as an induced subgraph. Barrus, Kumbhat, and Hartke [M. D…
Uniqueness and minimal obstructions 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…
Hereditary unigraphs and Erdős--Gallai equalities
Michael D. Barrus
We give characterizations of the structure and degree sequences of hereditary unigraphs, those graphs for which every induced subgraph is the unique realization of its degree seque…