The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The author not only provides a thorough description of the theory, but also details its applications, on the one hand to the construction of graph algorithms, and, on the other to the extension of formal language theory to finite graphs. Consequently the book will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory.

/pdf/graph-structure-and-monadic-second-order-logic-a-language-zne8xgxf5p.pdf

Graph Structure and Monadic Second-Order Logic: A Language-Theoretic Approach

A new parameter optimization method for a hybrid quantum-classical algorithm shows how it can exploit novel mechanisms to speed up computational time by orders of magnitude.

https://link.aps.org/pdf/10.1103/PhysRevX.10.021067

Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term Devices

This book is the first and only one of its kind on the topic of Cops and Robbers games, and more generally, on the field of vertex pursuit games on graphs The book is written in a lively and highly readable fashion, which should appeal to both senior undergraduates and experts in the field (and everyone in between) One of the main goals of the book is to bring together the key results in the field; as such, it presents structural, probabilistic, and algorithmic results on Cops and Robbers games Several recent and new results are discussed, along with a comprehensive set of references The book is suitable for self-study or as a textbook, owing in part to the over 200 exercises The reader will gain insight into all the main directions of research in the field and will be exposed to a number of open problems

The Game of Cops and Robbers on Graphs

On the complexity of reconfiguration problems

Graph-Theoretic Concepts in Computer Science

The problem of computing the chromatic number of a P5-free graph (a graph which contains no path on 5 vertices as an induced subgraph) is known to be NP-hard. However, we show that for every fixed integer k, there exists a polynomial-time algorithm determining whether or not a P5-free graph admits a k-coloring, and finding one, if it does.

/pdf/deciding-k-colorability-of-p-5-free-graphs-in-polynomial-21ee0ci08n.pdf

Deciding k -Colorability of P 5 -Free Graphs in Polynomial Time

Recent developments on graphs of bounded clique-width

Vertex and edge colorability are two graph problems that are NP-hard in general. We show that both problems remain difficult even for graphs without 

short cycles, i.e., without cycles of length at most g 

for any particular value of g. On the contrary, for graphs without long cycles, both problems are shown to be

solvable in poynomial time.

https://cdm.ucalgary.ca/article/download/61890/46635

Coloring edges and vertices of graphs without short or long cycles

http://www.medvedevgroup.com/papers/shortest_path_academic_copy.pdf

Shortest paths between shortest paths

http://dspace.mit.edu/bitstream/handle/1721.1/73858/Demaine-Reconfiguration%20of%20list.pdf;sequence=1

Marcin Kamiński

Papers

Deciding k -Colorability of P 5 -Free Graphs in Polynomial Time

Recent developments on graphs of bounded clique-width

Coloring edges and vertices of graphs without short or long cycles

Shortest paths between shortest paths

Reconfiguration of list edge-colorings in a graph