Now showing items 1-7 of 7

    • Algebraic Analysis of Vertex-Distinguishing Edge-Colorings 

      Clark, David (University of Waterloo, 2006)
      Vertex-distinguishing edge-colorings (vdec colorings) are a restriction of proper edge-colorings. These special colorings require that the sets of edge colors incident to every vertex be distinct. This is a relatively ...
    • Approximately Coloring Graphs Without Long Induced Paths 

      Chudnovsky, Maria; Schaudt, Oliver; Spirkl, Sophie; stein, maya; Zhong, Mingxian (Springer Nature, 2019)
      It is an open problem whether the 3-coloring problem can be solved in polynomial time in the class of graphs that do not contain an induced path on t vertices, for fixed t. We propose an algorithm that, given a 3-colorable ...
    • Cliques, Degrees, and Coloring: Expanding the ω, Δ, χ paradigm 

      Kelly, Thomas (University of Waterloo, 2019-08-09)
      Many of the most celebrated and influential results in graph coloring, such as Brooks' Theorem and Vizing's Theorem, relate a graph's chromatic number to its clique number or maximum degree. Currently, several of the most ...
    • Convex Algebraic Geometry Approaches to Graph Coloring and Stable Set Problems 

      Romero Barbosa, Julian Ariel (University of Waterloo, 2021-08-23)
      The objective of a combinatorial optimization problem is to find an element that maximizes a given function defined over a large and possibly high-dimensional finite set. It is often the case that the set is so large that ...
    • List 3-Coloring Graphs with No Induced P6+rP3 

      Chudnovsky, Maria; Huang, Shenwei; Spirkl, Sophie; Zhong, Mingxian (Springer Nature, 2021-01-01)
      For an integer t, we let Pt denote the t-vertex path. We write H+G for the disjoint union of two graphs H and G, and for an integer r and a graph H, we write rH for the disjoint union of r copies of H. We say that a graph ...
    • Partitioning Pauli Operators: in Theory and in Practice 

      Jena, Andrew (University of Waterloo, 2019-09-04)
      Measuring the expectation value of Pauli operators on prepared quantum states is a fundamental task in the variational quantum eigensolver. Simultaneously measuring sets of operators allows for fewer measurements and an ...
    • Thomassen’s 5-Choosability Theorem Extends to Many Faces 

      Nevin, Joshua (University of Waterloo, 2021-09-10)
      We prove in this thesis that planar graphs can be L-colored, where L is a list-assignment in which every vertex has a 5-list except for a collection of arbitrarily large faces which have 3-lists, as long as those faces ...


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