Now showing items 21-40 of 2173

    • Sandwich and probe problems for excluding paths 

      Figueiredo, Celina Miraglia Herrera de; Spirkl, Sophie (Elsevier, 2018-12-31)
      Let Pk denote an induced path on k vertices. For k ≥ 5, we show that the Pk-free sandwich problem, partitioned probe problem, and unpartitioned probe problem are NP-complete. For k ≤ 4, it is known that the Pk-free sandwich ...
    • Minimal induced subgraphs of two classes of 2-connected non-Hamiltonian graphs 

      Cheriyan, Joseph; Hajebi, Sepehr; Qu, Zishen; Spirkl, Sophie (Elsevier, 2022-07)
      In 1981, Duffus, Gould, and Jacobson showed that every connected graph either has a Hamiltonian path, or contains a claw (K1,3) or a net (a fixed six-vertex graph) as an induced subgraph. This implies that subject to being ...
    • On symmetric intersecting families of vectors 

      Eberhard, Sean; Kahn, Jeff; Narayanan, Bhargav; Spirkl, Sophie (Cambridge University Press, 2021-11)
      A family of vectors in [k]n is said to be intersecting if any two of its elements agree on at least one coordinate. We prove, for fixed k ≥ 3, that the size of any intersecting subfamily of [k]n invariant under a transitive ...
    • Modular relations of the Tutte symmetric function 

      Crew, Logan; Spirkl, Sophie (Elsevier, 2022-04)
      For a graph G, its Tutte symmetric function XBG generalizes both the Tutte polynomial TG and the chromatic symmetric function XG. We may also consider XB as a map from the t-extended Hopf algebra G[t] of labelled graphs ...
    • Finding Large H-Colorable Subgraphs in Hereditary Graph Classes 

      Chudnovsky, Maria; King, Jason; Pilipczuk, Michał; Rzążewski, Paweł; Spirkl, Sophie (Society for Industrial and Applied Mathematics, 2021-10-14)
      We study the Max Partial H-Coloring problem: given a graph G, find the largest induced subgraph of G that admits a homomorphism into H, where H is a fixed pattern graph without loops. Note that when H is a complete 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, ...
    • Pure Pairs VI. Excluding an Ordered Tree. 

      Scott, Alex; Seymour, Paul; Spirkl, Sophie (Society for Industrial and Applied Mathematics Journal on Discrete Mathematics, 2022-01)
      A pure pair in a graph G is a pair (Z1,Z2) of disjoint sets of vertices such that either every vertex in Z1 is adjacent to every vertex in Z2, or there are no edges between Z1 and Z2. With Maria Chudnovsky, we recently ...
    • The Pivot of Athwartedness: Roy Kiyooka's "Pacific Windows" 

      Austen, Veronica J. (Guernica, 2020)
      Published as a full issue of The Capilano Review in August 1990, Roy Kiyooka’s “Pacific Windows” exists on the periphery of Kiyooka’s canon. Despite the various ways in which this text could be considered the culmination ...
    • Plethysms of Chromatic and Tutte Symmetric Functions 

      Spirkl, Sophie; Crew, Logan (The Electronic Journal of Combinatorics, 2022)
      Plethysm is a fundamental operation in symmetric function theory, derived directly from its connection with representation theory. However, it does not admit a simple combinatorial interpretation, and finding coefficients ...
    • 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 ...
    • Four-coloring P6-free graphs 

      Chudnovsky, Maria; Spirkl, Sophie; Zhong, Mingxian (Association for Computing Machinery, 2019)
      In this paper we present a polynomial time algorithm for the 4-COLORING PROBLEM and the 4-PRECOLORING EXTENSION problem restricted to the class of graphs with no induced six-vertex path, thus proving a conjecture of Huang. ...
    • 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 ...
    • Polynomial bounds for chromatic number II: Excluding a star-forest 

      Scott, Alex; Seymour, Paul; Spirkl, Sophie (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 

      Scott, Alex; Seymour, Paul; Spirkl, Sophie (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 

      Chudnovsky, Maria; Spirkl, Sophie; Zerbib, Shira (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 

      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.
    • 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 ...
    • H-colouring Pt-free graphs in subexponential time 

      Groenland, Carla; Okrasa, Karolina; Rzążewski, Paweł; Scott, Alex; Seymour, Paul; Spirkl, Sophie (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 

      Chudnovsky, Maria; Liu, Chun-Hung; Schaudt, Oliver; Spirkl, Sophie; Trotignon, Nicolas; Vušković, Kristina (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 

      Chudnovsky, Maria; Scott, Alex; Seymour, Paul; Spirkl, Sophie (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.

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