Browsing Waterloo Research by Author "Spirkl, Sophie"
Now showing items 1-20 of 67
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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 ... -
Approximately Coloring Graphs Without Long Induced Paths
Chudnovsky, Maria; Schaudt, Oliver; Spirkl, Sophie; stein, maya; Zhong, Mingxian (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 ... -
Binary Adder Circuits of Asymptotically Minimum Depth, Linear Size, and Fan-Out Two
Held, Stephan; Spirkl, Sophie (Association for Computing Machinery, 2018-01)We consider the problem of constructing fast and small binary adder circuits. Among widely used adders, the Kogge-Stone adder is often considered the fastest, because it computes the carry bits for two n-bit numbers (where ... -
Bipartite graphs with no K6 minor
Chudnovsky, Maria; Scott, Alex; Seymour, Paul; Spirkl, Sophie (Elsevier, 2024-01)A theorem of Mader shows that every graph with average degree at least eight has a K6 minor, and this is false if we replace eight by any smaller constant. Replacing average degree by minimum degree seems to make little ... -
Caterpillars in Erdős–Hajnal
Liebenau, Anita; Pilipczuk, Marcin; Seymour, Paul; Spirkl, Sophie (Elsevier, 2019-05)Let T be a tree such that all its vertices of degree more than two lie on one path; that is, T is a caterpillar subdivision. We prove that there exists ε > 0 such that for every graph G with |V(G)| ≥ 2 not containing T as ... -
Colouring perfect graphs with bounded clique number
Chudnovsky, Maria; Lagoutte, Aurélie; Seymour, Paul; Spirkl, Sophie (Elsevier, 2017-01)A graph is perfect if the chromatic number of every induced subgraph equals the size of its largest clique, and an algorithm of Grötschel, Lovász, and Schrijver [9] from 1988 finds an optimal colouring of a perfect graph ... -
A Complete Multipartite Basis for the Chromatic Symmetric Function
Crew, Logan; Spirkl, Sophie (Society for Industrial and Applied Mathematics, 2021-11-15)In the vector space of symmetric functions, the elements of the basis of elementary symmetric functions are (up to a factor) the chromatic symmetric functions of disjoint unions of cliques. We consider their graph complements, ... -
Complexity Dichotomy for List-5-Coloring with a Forbidden Induced Subgraph
Hajebi, Sepehr; Li, Yanjia; Spirkl, Sophie (Society for Industrial and Applied Mathematics, 2022-08-30)For a positive integer r and graphs G and H, we denote by G+H the disjoint union of G and H and by rH the union of r mutually disjoint copies of H. Also, we say G is H-free if H is not isomorphic to an induced subgraph of ... -
Complexity of Ck-Coloring in Hereditary Classes of Graphs
Chudnovsky, Maria; Huang, Shenwei; Rzążewski, Paweł; Spirkl, Sophie; Zhong, Mingxian (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 ... -
Complexity of Ck-coloring in hereditary classes of graphs
Chudnovsky, Maria; Huang, Shenwei; Rzazewski, Pawel; Spirkl, Sophie; Zhong, Mingxian (Elsevier, 2023-06)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 ... -
Concatenating Bipartite Graphs
Chudnovsky, Maria; Hompe, Patrick; Scott, Alex; Seymour, Paul; Spirkl, Sophie (The Electronic Journal of Combinatorics, 2022)Let x, y E (0, 1], and let A, B, C be disjoint nonempty stable subsets of a graph G, where every vertex in A has at least x |B| neighbors in B, and every vertex in B has at least y|C| neighbors in C, and there are no edges ... -
A Counterexample to a Conjecture About Triangle-Free Induced Subgraphs of Graphs with Large Chromatic Number
Carbonero, Alvaro; Hompe, Patrick; Moore, Benjamin; Spirkl, Sophie (Elsevier ScienceDirect, 2023-01)We prove that for every n, there is a graph G with χ(G) ≥ n and ω(G) ≤ 3 such that every induced subgraph H of G with ω(H) ≤ 2 satisfies χ(H) ≤ 4.This disproves a well-known conjecture. Our construction is a digraph with ... -
A deletion–contraction relation for the chromatic symmetric function
Crew, Logan; Spirkl, Sophie (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 ... -
Detecting an Odd Hole
Chudnovsky, Maria; Scott, Alex; Seymour, Paul; Spirkl, Sophie (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. -
Digraphs with All Induced Directed Cycles of the Same Length are not → χ -Bounded
Carbonero, Alvaro; Hompe, Patrick; Moore, Benjamin; Spirkl, Sophie (2022-10-07)For t > 2, let us call a digraph D t-chordal if all induced directed cycles in D have length equal to t. In an earlier paper, we asked for which t it is true that t-chordal graphs with bounded clique number have bounded ... -
Disproportionate Division
Crew, Logan; Narayanan, Bhargav; Spirkl, Sophie (Wiley, 2020-10-01)We study the disproportionate version of the classical cake-cutting problem: how efficiently can we divide a cake, here [0,1], among n ≥ 2 agents with different demands α1, α2,..., αn summing to 1? When all the agents have ... -
Entropic Matroids and Their Representation
Abbe, Emmanuel; Spirkl, Sophie (Multidisciplinary Digital Publishing Institute, 2019)This paper investigates entropic matroids, that is, matroids whose rank function is given as the Shannon entropy of random variables. In particular, we consider p-entropic matroids, for which the random variables each have ... -
Even pairs and prism corners in square-free Berge graphs
Chudnovsky, Maria; Maffray, Frédéric; Seymour, Paul; Spirkl, Sophie (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. -
Fast Prefix Adders for Non-uniform Input Arrival Times
Held, Stephan; Spirkl, Sophie (Springer Nature, 2017)We consider the problem of constructing fast and small parallel prefix adders for non-uniform input arrival times. In modern computer chips, adders with up to hundreds of inputs occur frequently, and they are often embedded ... -
Finding an induced path that is not a shortest path
Berger, Eli; Seymour, Paul; Spirkl, Sophie (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.