University of Waterloo
This institution-wide community is designed to house collections of Waterloo created electronic research that span the institution or are not logically subsumed by a single faculty sub-community.
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Posturing Horses: Xenophon on Biomechanical Soundness in The Art of Horsemanship
(University of Waterloo, 2022-08-12)As early as the Bronze Age, ancient Greek horses shared in the social status of the military elite. The ritual inclusion of horses and their equipment in burial practices from the Bronze Age to the Classical period marked ... -
Multiscale Modelling of Structural Transformation in Metal Nanocatalysts for CO2 Electroreduction
(University of Waterloo, 2022-08-12)The precise control of nanostructure and surface atomic arrangement can be used to tune the electrocatalytic properties of materials and improve their performance. Unfortunately, the long-term structural stability of ... -
Methods in Modelling of Composite Materials with Microstructure
(University of Waterloo, 2022-08-12)Composite material properties are dependent on their microstructure. To adequately model these materials, a revised formulation of elasticity that accounts for microstructural effects must be considered. Size dependent ... -
Worth the Effort? The Effects of Task-Centrality, Annoyance, and Arrogance on Manager Effort Allocation During Feedback-Seeking Episodes
(University of Waterloo, 2022-08-12)Employees seek feedback from managers to reduce work-related ambiguity. However, managers typically have other competing demands on their time, and as such, may not allocate sufficient effort to providing feedback. To this ... -
Wormlike Chain Polymers Under External Fields with Applications to Nanotechnology
(University of Waterloo, 2022-08-12)Polymers are long molecular chains formed from smaller molecular units called monomers. Polymers display interesting macroscopic properties, are ubiquitous in everyday materials, and are also important biomolecules among ... -
Approximately Coloring Graphs Without Long Induced Paths
(Springer Nature, 2017)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 ... -
Polynomial bounds for chromatic number II: Excluding a star-forest
(Wiley, 2022-10)The Gyárfás–Sumner conjecture says that for every forest H, there is a function fH such that if G is H-free then x(G) ≤ fH(w(G)) (where x,w are the chromatic number and the clique number of G). Louis Esperet conjectured ... -
Polynomial bounds for chromatic number. III. Excluding a double star
(Wiley, 2022-10)A “double star” is a tree with two internal vertices. It is known that the Gyárfás-Sumner conjecture holds for double stars, that is, for every double star H, there is a function fH such that if G does not contain H as ... -
Piercing axis-parallel boxes
(The Electronic Journal of Combinatorics, 2018)Let F be a finite family of axis-parallel boxes in Rd such that F contains no k + 1 pairwise disjoint boxes. We prove that if F contains a subfamily M of k pairwise disjoint boxes with the property that for every F E F ... -
Even pairs and prism corners in square-free Berge graphs
(Elsevier, 2018-07)Let G be a Berge graph such that no induced subgraph is a 4-cycle or a line-graph of a bipartite subdivision of K4. We show that every such graph G either is a complete graph or has an even pair. -
Complexity of Ck-Coloring in Hereditary Classes of Graphs
(Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2019)For a graph F, a graph G is F-free if it does not contain an induced subgraph isomorphic to F. For two graphs G and H, an H-coloring of G is a mapping f : V (G) --> V (H) such that for every edge uv E(G) it holds that ... -
H-colouring Pt-free graphs in subexponential time
(Elsevier, 2019-08-31)A graph is called Pt-free if it does not contain the path on t vertices as an induced subgraph. Let H be a multigraph with the property that any two distinct vertices share at most one common neighbour. We show that the ... -
Triangle-free graphs that do not contain an induced subdivision of K4 are 3-colorable
(Wiley, 2019-10)We show that triangle-free graphs that do not contain an induced subgraph isomorphic to a subdivision of K4 are 3-colorable. This proves a conjecture of Trotignon and Vušković. -
Induced subgraphs of graphs with large chromatic number. VIII. Long odd holes
(Elsevier, 2020-01)We prove a conjecture of András Gyárfás, that for all k, l, every graph with clique number at most κ and sufficiently large chromatic number has an odd hole of length at least ℓ. -
Detecting an Odd Hole
(Association for Computing Machinery, 2020-02)We give a polynomial-time algorithm to test whether a graph contains an induced cycle with length more than three and odd. -
A deletion–contraction relation for the chromatic symmetric function
(Elsevier, 2020-10)We extend the definition of the chromatic symmetric function XG to include graphs G with a vertex-weight function w : V (G) --> N. We show how this provides the chromatic symmetric function with a natural deletion-contraction ... -
List 3-coloring Pt-free graphs with no induced 1-subdivision of K1,s
(Elsevier, 2020-11)Let s and t be positive integers. We use Pt to denote the path with t vertices and K1,s to denote the complete bipartite graph with parts of size 1 and s respectively. The one-subdivision of K1,s is obtained by replacing ... -
Pure pairs. I. Trees and linear anticomplete pairs
(Elsevier, 2020-12-02)The Erdős-Hajnal conjecture asserts that for every graph H there is a constant c > 0 such that every graph G that does not contain H as an induced subgraph has a clique or stable set of cardinality at least |G|c. In this ... -
Finding an induced path that is not a shortest path
(Elsevier, 2021-07)We give a polynomial-time algorithm that, with input a graph G and two vertices u; v of G, decides whether there is an induced uv-path that is longer than the shortest uv-path. -
A note on simplicial cliques
(Elsevier, 2021-09)Motivated by an application in condensed matter physics and quantum information theory, we prove that every non-null even-hole-free claw-free graph has a simplicial clique, that is, a clique K such that for every vertex v ...
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