Browsing Waterloo Research by Author "Spirkl, Sophie"

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 ...

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. ...

Four-coloring P6-free graphs. I. Extending an excellent precoloring.

Chudnovsky, Maria; Spirkl, Sophie; Zhong, Mingxian (Society for Industrial and Applied Mathematics, 2024)

This is the first paper in a series whose goal is to give 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, ...

Four-coloring P6-free graphs. II. Finding an excellent precoloring.

Chudnovsky, Maria; Spirkl, Sophie; Zhong, Mingxian (Society for Industrial and Applied Mathematics, 2024)

This is the second paper in a series of two. The goal of the series is to give a polynomial-time algorithm for the 4-coloring problem and the 4-precoloring extension problem restricted to the class of graphs with no induced ...

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 ...

Induced subgraphs and tree decompositions II. Toward walls and their line graphs in graphs of bounded degree.

Abrishami, Tara; Chudnovsky, Maria; Dibek, Cemil; Hajebi, Sepehr; Rzqzewski, Pawel; Spirkl, Sophie; Vuskovic, Kristina (Elsevier, 2024-01)

This paper is motivated by the following question: what are the unavoidable induced subgraphs of graphs with large treewidth? Aboulker et al. made a conjecture which answers this question in graphs of bounded maximum ...

Induced Subgraphs and Tree Decompositions III. Three-Path-Configurations and Logarithmic Treewidth.

Abrishami, Tara; Chudnovsky, Maria; Hajebi, Sepehr; Spirkl, Sophie (Advances in Combinatorics, 2022-09-09)

A theta is a graph consisting of two non-adjacent vertices and three internally disjoint paths between them, each of length at least two. For a family H of graphs, we say a graph G is H-free if no induced subgraph of G is ...

Induced Subgraphs and Tree Decompositions IV. (Even Hole, Diamond, Pyramid)-Free Graphs

Abrishami, Tara; Chudnovsky, Maria; Hajebi, Sepehr; Spirkl, Sophie (Electronic Journal of Combinatorics, 2023-06-16)

A hole in a graph G is an induced cycle of length at least four, and an even hole is a hole of even length. The diamond is the graph obtained from the complete graph K4 by removing an edge. A pyramid is a graph consisting ...

Induced subgraphs and tree decompositions VII. Basic obstructions in H-free graphs.

Abrishami, Tara; Alecu, Bogdan; Chudnovsky, Maria; Hajebi, Sepehr; Spirkl, Sophie (Elsevier, 2024-01)

We say a class C of graphs is clean if for every positive integer t there exists a positive integer w(t) such that every graph in C with treewidth more than w(t) contains an induced subgraph isomorphic to one of the ...

Induced Subgraphs and Tree Decompositions VIII: Excluding a Forest in (Theta, Prism)-Free Graphs

Abrishami, Tara; Alecu, Bogdan; Chudnovsky, Maria; Hajebi, Sepehr; Spirkl, Sophie (Springer, 2024-04-08)

Given a graph H, we prove that every (theta, prism)-free graph of sufficiently large treewidth contains either a large clique or an induced subgraph isomorphic to H, if and only if H is a forest.

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.

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 ...

List 3-coloring Pt-free graphs with no induced 1-subdivision of K1,s

Chudnovsky, Maria; Spirkl, Sophie; Zhong, Mingxian (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 ...

List-3-Coloring Ordered Graphs with a Forbidden Induced Subgraph

Hajebi, Sepehr; Li, Yanjia; Spirkl, Sophie (Society for Industrial and Applied Mathematics, 2024-03)

Abstract. The List-3-Coloring Problem is to decide, given a graph G and a list L(v) ⊆ {1, 2, 3} of colors assigned to each vertex v of G, whether G admits a proper coloring ϕ with ϕ(v) ∈ L(v) for every vertex v of G, and ...

Minimal induced subgraphs of the class of 2-connected non-Hamiltonian wheel-free graphs

Chaniotis, Aristotelis; Qu, Zishen; Spirkl, Sophie (Elsevier ScienceDirect, 2022-12-29)

Given a graph G and a graph property P we say that G is minimal with respect to P if no proper induced subgraph of G has the property P. An HC-obstruction is a minimal 2-connected non-Hamiltonian graph. Given a graph H, a ...

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 ...

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 ...

A note on simplicial cliques

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

On Aharoni’s rainbow generalization of the Caccetta–Häggkvist conjecture

Hompe, Patrick; Pelikánová, Petra; Pokorná, Aneta; Spirkl, Sophie (Elsevier, 2021-05-01)

For a digraph G and v is an element of V(G), let delta(+)(v) be the number of out-neighbors of v in G. The Caccetta-Haggkvist conjecture states that for all k >= 1, if G is a digraph with n = |V(G)| such that delta(+)(v) ...

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 ...