DisCoMath Seminar: Quantum Coloring of Graphs
DisCoMath Seminar
Quantum Coloring of Graphs
Tess Collins
Mathematical Modeling Ph.D. Student
Rochester Institute of Technology
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Abstract:
Graph coloring is one of the most well-known areas of graph theory, and the seductiveness of a graph's chromatic number has incited many extensions and relaxations of this parameter. One such extension is the "quantum chromatic number" of a graph. In a quantum 𝑐-coloring of a graph 𝐺, each vertex is assigned a set of 𝑐 orthogonal projectors such that two important properties are satisfied: 1) Completeness: the matrices assigned to each vertex sum to the identity, and 2) Orthogonality: respective matrices of adjacent vertices are orthogonal. We will talk about the "physics-y" origin of this version of graph coloring, look at some fun examples and known properties of quantum colorings of graphs, discuss the two existing methods for constructing a quantum coloring of a graph, and touch on how we might extend these methods.
Intended Audience:
All are Welcome!
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