Browsing Waterloo Research by Author "Chudnovsky, Maria"
Now showing items 1-20 of 36
-
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 ... -
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 ... -
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 ... -
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 ... -
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. -
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. -
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 ... -
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 ...