Diestel Graph Theory Explained

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Diestel-Graph-Theory-Explained

Graphs are an effective way to communicate information. They are used in everything, from genetic studies to information graphics that are posted to articles on the internet. Reinhard Diestel wrote about the various aspects of graph theory in mathematics that incorporates flows, connectivity, coloring, matching, planarity, and more.

Deistel separated each theory into a specific chapter. He introduces the graph theory variation, discusses common questions that are asked, and offers simplified proofs so anyone can follow along with the idea without having a full grasp of the intentions of the theorist.

Therefore, Diestal explains the graph theories that others have introduced into the world of mathematics instead of creating one of his own. Graph Theory is a graduate-level text that has been published in its 5th edition as of 2016. More information can be accessed at diestel-graph-theory.com.

Getting to Know Reinhard Diestel

Reinhard Diestel was born in 1959. He is a German mathematician who received a fellowship at Trinity College in Cambridge from 1983-1986. He was also the recipient of a Knight’s Prize. One of his first contributions to a greater understanding of mathematics was the publication of Simplicial Decompositions and Universal Graphs, which he co-authored with Bela Bollobas in 1986.

Following his time at Trinity College, Diestel because a fellow at St. John’s College in 1990, remaining in Cambridge. He also qualified as a professor of mathematics at the University of Hamburg during this period. With these successes, Diestel moved his studies to the United States and the University of Bielefeld. He studied on the Heisenberg scholarship at the University of Oxford in 1993.

From 1994-1996, Diestel would work as a professor at the Chemnitz University of Technology. Since 1996, he has focused on his teaching position in Hamburg.

Why Did Diestel Create Graph Theory?

In mathematics, changes that affect previous materials are rare. There are local improvements made to teach, polish, or consolidate the materials that professors pass along to students, however, and that is what makes Graph Theory such a unique textbook. Diestel includes many of his own personal notes and observations in how to teach advanced mathematics from his personal perspectives.

As he discussed in the 3rd edition of his book, published in 2005.

“Most of these [local additions] developed from my own notes, penciled in the margin as I prepare to teach from the book. They typically complement an important, but technical proof, when I felt that its essential ideas might get overlooked in the formal write-up. For example, the proof of the Erdos-Stone theorem now has an informal post-mortem that looks at how exactly the regularity lemma comes to be applied in it.”

What makes Diestel’s observations so relevant and effective is that he begins his discussions on the main idea of each graph theory instead of starting with a formal proof. That makes it possible for students to understand the concepts and logic that go into the theorems that are being discussed. From the main idea, he eventually arrives at the parameters that must be declared, and that makes it easier for the formal proofs to be utilized.

Expectations of Diestel’s Graph Theory

Like many textbooks, Diestel begins his work by taking students through the basics of graphs. The reader is introduced to the degree of a vertex, paths and cycles, and connectivity within the first 10 pages of his textbook. From there, he covers bipartite graphs, Euler tours, and even covers some linear algebra.

After this first chapter, Diestel then moves to matching, covering, and packing. That includes matching in general graphs and bipartite graphs. He also makes recommendations to teachers who might be using his textbook, showing them which sections or subjects are recommended for a first course to cover.

Diestel also covers planar graphs, coloring, flows, extremal graph theory, the Ramsey Theory for graphs, infinite graphs, and Hamilton cycles.

Including infinite sets, surfaces, and the indexes involved, Graph Theory is more than 400 pages of instructional content to cover.

For those who are seeking a career in mathematics, Diestel’s Graph Theory is an excellent teaching resource that explains core concepts on a relatable level. With older versions of this textbook available for free online as a PDF, his observations are accessible to everyone today.