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Found 4 Results
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Matching Complexes of Graphs

The matching complex of a graph is the simplicial complex whose vertex set is the set of edges of the graph with a face for each independent set of edges. The perfect matching complex is the subcomplex generated by perfect matchings (independent sets of edges that cover all vertices of the graph). This talk presents a number of recent results on the [Read More...]

Presenter: Margaret Bayer, University of Kansas
Authors: Margaret Bayer, Marija Jeli'c Milutinovi'c, and Julianne Vega
Symposium Year: 2022
Session: Advances in Combinatorics
Presentation Time: June 17, 2022; 3:30 pm

The Distinguishing Chromatic Number of a Poset

A coloring of the points of a poset P is proper if each color class induces an antichain, and distinguishing if the only automorphism of P that preserves colors is the identity. The distinguishing chromatic number of a poset, is the least integer for which there is a coloring of P that is both proper and distinguishing. In this talk we determine the [Read More...]

Presenter: Ann Trenk, Wellesley College
Authors: Karen Collins and Ann Trenk
Symposium Year: 2022
Session: Advances in Combinatorics
Presentation Time: June 17, 2022; 3:55 pm

The Distinguishing Chromatic Number of a Poset, Part II

A coloring of the points of a poset is $\textit{proper}$ if each color class induces an antichain, and $\textit{distinguishing}$ if only the identity automorphism of $P$ preserves the colors. The address $\textit{distinguishing chromatic number}$ of a poset, $\chi_D(P)$, is the smallest number of colors for which there is a coloring that is both proper and [Read More...]

Presenter: Karen L. Collins, Wesleyan University
Authors: Karen L. Collins, Ann N. Trenk
Symposium Year: 2022
Session: Advances in Combinatorics
Presentation Time: June 17, 2022; 4:20 pm

Splitters and Decomposers for Binary Matroids

Matroids are a geometry defined by certain combinatorial axioms and like most geometries, some matroids are more important than others. Consider a class of matroids closed under minors. A splitter for the minor-closed class is a 3-connected matroid N in the class, such that no 3-connected matroid in the class has a proper N-minor. A 3-decomposer for the [Read More...]

Presenter: Sandra Kingan, Brooklyn College and the Graduate Center, CUNY
Authors: Sandra Kingan
Symposium Year: 2022
Session: Advances in Combinatorics
Presentation Time: June 17, 2022; 4:45 pm
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