Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, October 9, 2019.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    September 2019          October 2019          November 2019
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1  2  3  4  5  6  7          1  2  3  4  5                   1  2
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Wednesday, October 9, 2019

4:00 pm in 245 Altgeld Hall,Wednesday, October 9, 2019

#### An overview of Erdős-Rothschild problems and their rainbow variants

###### Lina Li

Abstract: In 1974, Erdős and Rothchild conjectured that the complete bipartite graph has the maximum number of two-edge-colorings without monochromatic triangles over all n-vertex graphs. Since then, this new class of colored extremal problems has been extensively studied by many researchers on various discrete structures, such as graphs, hypergraphs, boolean lattices and sets. In this talk, I would like to give an overview of some past results on this topic. The second half of this talk is to investigate the rainbow variants of the Erdős-Rothschild problem. Our first main result, confirming conjectures of Benevides, Hoppen and Sampaio, and Hoppen, Lefmann, and Odermann, completes the characterization of the extremal graphs for the edge-colorings without rainbow triangles. We also studied a similar question on sum-free sets, in which we describe the extremal configurations for the colorings of integers without rainbow sums.

4:00 pm in Altgeld Hall,Wednesday, October 9, 2019

#### Disability Allyship and DRES Information

Abstract: For all faculty members and graduate students - DRES staff members will provide practical information on making classroom instruction as accessible as possible to all students and on DRES policies and procedures.