An extensive English language bibliography on graph theory and its applications

Bibliography on graph theory and its application

An extensive English language bibliography on graph theory and its applications, supplement 1

Graph theory and its applications - bibliography, supplement

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum

Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization

International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM

Algorithmic Graph Theory

The main focus of this workshop was on mathematical techniques needed for the development of efficient solutions and algorithms for computationally difficult graph problems. The techniques studied at the workshhop included: the probabilistic method and randomized algorithms, approximation and optimization, structured families of graphs and approximation algorithms for large problems. The workshop Algorithmic Graph Theory was attended by 46 participants, many of them being young researchers. In 15 survey talks an overview of recent developments in Algorithmic Graph Theory was given. These talks were supplemented by 10 shorter talks and by two special sessions

Graph kernel extensions and experiments with application to molecule classification, lead hopping and multiple targets

The discovery of drugs that can effectively treat disease and alleviate pain is one of the core challenges facing modern medicine. The tools and techniques of machine learning have perhaps the greatest potential to provide a fast and efficient route toward the fabrication of novel and effective drugs. In particular, modern structured kernel methods have been successfully applied to range of problem domains and have been recently adapted for graph structures making them directly applicable to pharmaceutical drug discovery. Specifically graph structures have a natural fit with molecular data, in that a graph consists of a set of nodes that represent atoms that are connected by bonds. In this thesis we use graph kernels that utilize three different graph representations: molecular, topological pharmacophore and reduced graphs. We introduce a set of novel graph kernels which are based on a measure of the number of finite walks within a graph. To calculate this measure we employ a dynamic programming framework which allows us to extend graph kernels so they can deal with non-tottering, softmatching and allows the inclusion of gaps. In addition we review several graph colouring methods and subsequently incorporate colour into our graph kernels models. These kernels are designed for molecule classification in general, although we show how they can be adapted to other areas in drug discovery. We conduct three sets of experiments and discuss how our augmented graph kernels are designed and adapted for these areas. First, we classify molecules based on their activity in comparison to a biological target. Second, we explore the related problem of lead hopping. Here one set of chemicals is used to predict another that is structurally dissimilar. We discuss the problems that arise due to the fact that some patterns are filtered from the dataset. By analyzing lead hopping we are able to go beyond the typical cross-validation approach and construct a dataset that more accurately reflect real-world tasks. Lastly, we explore methods of integrating information from multiple targets. We test our models as a multi-response problem and later introduce a new approach that employs Kernel Canonical Correlation Analysis (KCCA) to predict the best molecules for an unseen target. Overall, we show that graph kernels achieve good results in classification, lead hopping and multiple target experiments

Algebraic and combinatorial aspects of incidence groups and linear system non-local games arising from graphs

To every linear binary-constraint system (LinBCS) non-local game, there is an associated algebraic object called the solution group. Cleve, Liu, and Slofstra showed that a LinBCS game has a perfect quantum strategy if and only if an element, denoted by $J$, is non-trivial in this group. In this work, we restrict to the set of graph-LinBCS games, which arise from $\mathbb{Z}_2$-linear systems $Ax=b$, where $A$ is the incidence matrix of a connected graph, and $b$ is a (non-proper) vertex $2$-colouring. In this context, Arkhipov's theorem states that the corresponding graph-LinBCS game has a perfect quantum strategy, and no perfect classical strategy, if and only if the graph is non-planar and the $2$-colouring $b$ has odd parity. In addition to efficient methods for detecting quantum and classical strategies for these games, we show that computing the classical value, a problem that is NP-hard for general LinBCS games can be done efficiently. In this work, we describe a graph-LinBCS game by a $2$-coloured graph and call the corresponding solution group a graph incidence group. As a consequence of the Robertson-Seymour theorem, we show that every quotient-closed property of a graph incidence group can be expressed by a finite set of forbidden graph minors. Using this result, we recover one direction of Arkhipov's theorem and derive the forbidden graph minors for the graph incidence group properties: finiteness, and abelianness. Lastly, using the representation theory of the graph incidence group, we discuss how our graph minor criteria can be used to deduce information about the perfect strategies for graph-LinBCS games