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On coloring problems with local constraints

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The Power of Two Matrices in Spectral Algorithms for Community Recovery

Colin Peter Sandon

Spectral algorithms are some of the main tools in optimization and inference problems on graphs. Typically, the graph is encoded as a matrix and eigenvectors and eigenvalues of the matrix are then used to solve the given graph problem. Spectral algorithms ...

Ieee-Inst Electrical Electronics Engineers Inc2024

Recoloring subgraphs of K-2n for sports scheduling

Dominique de Werra

The exploration of one-factorizations of complete graphs is the foundation of some classical sports scheduling problems. One has to traverse the landscape of such one-factorizations by moving from one of those to a so-called neighbor one-factorization. Thi ...

ELSEVIER2021

Edge colorings of graphs without monochromatic stars

Abhishek Methuku

In this note, we improve on results of Hoppen, Kohayakawa and Lefmann about the maximum number of edge colorings without monochromatic copies of a star of a fixed size that a graph on n vertices may admit. Our results rely on an improved application of an ...

ELSEVIER2020

The Schur-Erdos problem for sesmi-algebraic colorings

János Pach

We considerm-colorings of the edges of a complete graph, where each color class is defined semi-algebraically with bounded complexity. The casem= 2 was first studied by Alon et al., who applied this framework to obtain surprisingly strong Ramsey-type resul ...

HEBREW UNIV MAGNES PRESS2020

Avoiding long Berge cycles: the missing casesk=r+1 andk=r+2

Abhishek Methuku

The maximum size of anr-uniform hypergraph without a Berge cycle of length at leastkhas been determined for allk >= r+ 3 by Furedi, Kostochka and Luo and fork

2020

Minimal graphs for 2-factor extension

Dominique de Werra

Let G = (V, E) be a simple loopless finite undirected graph. We say that G is (2-factor) expandable if for any non-edge uv, G + uv has a 2-factor F that contains uv. We are interested in the following: Given a positive integer n = vertical bar V vertical b ...

ELSEVIER2020

Distributed Coloring of Graphs with an Optimal Number of Colors

Etienne Michel François Bamas

This paper studies sufficient conditions to obtain efficient distributed algorithms coloring graphs optimally (i.e. with the minimum number of colors) in the LOCAL model of computation. Most of the work on distributed vertex coloring so far has focused on ...

SCHLOSS DAGSTUHL, LEIBNIZ CENTER INFORMATICS2019

On approximation algorithms and polyhedral relaxations for knapsack problems, and clustered planarity testing

Igor Malinovic

Knapsack problems give a simple framework for decision making. A classical example is the min-knapsack problem (MinKnap): choose a subset of items with minimum total cost, whose total profit is above a given threshold. While this model successfully general ...

EPFL2019

New Graph Algorithms via Polyhedral Techniques

Jakub Tarnawski

In this thesis we give new algorithms for two fundamental graph problems. We develop novel ways of using linear programming formulations, even exponential-sized ones, to extract structure from problem instances and to guide algorithms in making progress. S ...

EPFL2019

Vizing's celebrated theorem asserts that any graph of maximum degree Delta admits an edge coloring using at most Delta + 1 colors. In contrast, Bar-Noy, Motwani and Naor showed over a quarter century ago that the trivial greedy algorithm, which uses 2 Delt ...

IEEE COMPUTER SOC2019