Three graph families, 3 speakers, (iii) noun phrases (one talk)

Authors

• Mark Kayll, University of Montana, Missoula

Document Type

Presentation Abstract

Presentation Date

3-2-2026

Abstract

Sixty years ago, Jack Edmonds published an elegant characterization of a graph G's so-called ‘perfect matching polytope’ P (i.e., the convex hull of the characteristic vectors of G's perfect matchings). He described P polyhedrally as the set of nonnegative vectors ℝ^E(G) satisfying two families of constraints: ‘saturation’ and ‘blossom’. Mathematicians now call graphs for which the blossom constraints are essential Edmonds graphs and those for which the blossom constraints are implied by the others Egerváry graphs. As it turns out, the second graph class interacts nicely with more familiar ones; for example, bipartite graphs are Egerváry. This talk introduces these graph classes and shares a few results on Egerváry graphs that appeared recently in our Journal of Combinatorics article.

Additional Details

March 2, 2026 at 3:00 p.m. Math 103

Recommended Citation

Kayll, Mark, "Three graph families, 3 speakers, (iii) noun phrases (one talk)" (2026). Colloquia of the Department of Mathematical Sciences. 698.
https://scholarworks.umt.edu/mathcolloquia/698