Book Review: Topological graph theory

Topological Graph Theory A Survey

Extremal Graph Theory for Book-Embeddings

A book-embedding of a graph is a linear ordering of its vertices, and a partition of its edges into non-crossing sets (called pages). The pagenumber of a graph is the minimum number of pages for which it has a book-embedding. After introducing concepts relevant to book-embeddings and their applications, we will describe the main results on the pagenumber for classes of graphs, particularly resu...

Book Review: Contemporary Sensorimotor Theory

Consciousness, with its irreducible subjective character, was almost exclusively a philosophical topic until relatively recently. Today, however, the problem of explaining the felt quality of experience has also become relevant to science and engineering, including robotics andAI: “What would we have to build into a robot so that it really felt the touch of a finger, the redness of red, or the ...

Some Topological Methods in Graph Coloring Theory

Attempts to solve the famous Four Color Problem led to fruitful discoveries and rich coloring theories. In this talk, some old and some recent applications of tools from topology to graph coloring problems will be presented. In particular, the following subjects will be treated: The use of Euler’s formula and local planarity conditions, Kempe equivalence, homotopy, winding number and its higher...

Recent Results in Topological Graph Theory*

A graph G is usually defined as a finite collection V of points together with a collection X of lines, each of which joins two distinct points and no two of which join the same pair of points. This combinatorial definition asserts nothing about drawing graphs on surfaces such as the plane, sphere, torus, projective plane etc. The purpose of this lecture is to explore some of these topological a...