Meetings of the GSS will take place in Carver 401 on Fridays at 12:05 pm.
No meetings will take place during holidays.
9/11/26
Tony Vuolo
Title: On B-Colorings in Planar Graphs
Abstract: Gy\'arf\'as and S\'ark\"ozy [Studia Sci. Math. Hungar., 2023] defined a B-coloring of a graph to be a proper coloring of the edge set in which any $C_4$ is totally multicolored. Let $q_B(G)$ denote the minimum number of colors sufficient for a B-coloring of a graph $G$. In this talk, we prove that any planar graph $G$ with $\Delta=\Delta(G)$ and $\Delta_2=\Delta_2(G)$ has $q_B(G)\leq\Delta+\max\{\Delta_2,38\}$, refining a bound by Kong, Wang, and Zheng [J. Graph Theory, 2026].
9/18/26
Matt Burnham
Title: Small q-kernels in digraphs
Abstract: An independent set $Q$ of a digraph $D$ is called a $q$-kernel if all vertices of $D$ are reachable from $Q$ via a directed path of length at most $q$. The small quasikernel conjecture of Erdős and Székely posits that every digraph $D$ with minimum in-degree $\delta = 1$ has a $2$-kernel of size at most $\frac{1}{2}|V(D)|$. In 2024, Spiro posed a more general question: What is the smallest constant $c_{\delta,q}$ such that every digraph $D$ with minimum in-degree $\delta$ has a $q$-kernel of size at most $c_{\delta,q}|V(D)|$? We present new upper bounds for the constants $c_{\delta,q}$ and conjecture that a simple lower bound construction is tight when $q\geq 3$.
9/25/26
Billy Duckworth
Title: From Entropy to Continued Fractions and Knot Theory
Abstract: Starting with an attempt to define a notion of entropy for almost periodic dynamical systems, we will be forced to go on an unexpected journey into such topics as continued fractions and knot theory. Come ready to get tangled up in tangents!
10/2/26
Channing Bentz
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10/9/26
Khiem Nguyen
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10/16/26
Sophia Child
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10/23/26
Micah Coats
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10/30/26
Clay Higgins
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11/6/26
Nate Schacherl
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11/13/26
Nick Layman
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11/20/26
Ben Bridenbaugh
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11/27/26
Thanksgiving break!
12/4/26
Double Feature! Sycamore Herlihy and Austin Longin
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12/11/26
Hope Pungello
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