Browsing Mathematics (Faculty of) by Author "Chudnovsky, Maria"
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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 ... -
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 ... -
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. ... -
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 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 ... -
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 ... -
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 ... -
Proof of the Kalai-Meshulam conjecture
Chudnovsky, Maria; Scott, Alex; Seymour, Paul; Spirkl, Sophie (Springer Nature, 2020-07-01)Let G be a graph, and let fG be the sum of (−1)∣A∣, over all stable sets A. If G is a cycle with length divisible by three, then fG = ±2. Motivated by topological considerations, G. Kalai and R. Meshulam [8] made the ... -
Pure pairs. I. Trees and linear anticomplete pairs
Chudnovsky, Maria; Scott, Alex; Seymour, Paul; Spirkl, Sophie (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 ... -
Pure pairs. II. Excluding all subdivisions of a graph
Chudnovsky, Maria; Scott, Alex; Seymour, Paul; Spirkl, Sophie (Springer Nature, 2021-06-01)We prove for every graph H there exists ɛ > 0 such that, for every graph G with |G|≥2, if no induced subgraph of G is a subdivision of H, then either some vertex of G has at least ɛ|G| neighbours, or there are two disjoint ... -
Pure pairs. III. Sparse graphs with no polynomial-sized anticomplete pairs
Chudnovsky, Maria; Fox, Jacob; Scott, Alex; Seymour, Paul; Spirkl, Sophie (Wiley, 2020-11)A graph is H-free if it has no induced subgraph isomorphic to H, and |G| denotes the number of vertices of G. A conjecture of Conlon, Sudakov and the second author asserts that: - For every graph H, there exists ∈ > 0 ... -
The Sandwich Problem for Decompositions and Almost Monotone Properties
Chudnovsky, Maria; Figueiredo, Celina Miraglia Herrera de; Spirkl, Sophie (Springer Nature, 2018)We consider the graph sandwich problem and introduce almost monotone properties, for which the sandwich problem can be reduced to the recognition problem. We show that the property of containing a graph in C as an induced ...