Meridiankreisbeobachtungen des Kometen 1911 c (Brooks)

Brooks' Theorem and Beyond

We collect some of our favorite proofs of Brooks’ Theorem, highlighting advantages and extensions of each. The proofs illustrate some of the major techniques in graph coloring, such as greedy coloring, Kempe chains, hitting sets, and the Kernel Lemma. We also discuss standard strengthenings of vertex coloring, such as list coloring, online list coloring, and Alon–Tarsi orientations, since analo...

Books in Running Brooks

Maclyn McCarty (1911–2005)

The editorial board lost a real soul mate when Maclyn McCarty passed away on January 2nd at age 93. While attending the theater with friends, one of the many activities that he enjoyed, he collapsed. “Dr. Mac” was revered worldwide for his remarkable experiments that led to the identification of DNA as the genetic material. This totally unanticipated discovery, and the revolutionary 1944 paper ...

Simon Flexner, 1911

No Quantum Brooks' Theorem

First, I introduce quantum graph theory. I also discuss a known lower bound on the independence numbers and derive from it an upper bound on the chromatic numbers of quantum graphs. Then, I construct a family of quantum graphs that can be described as tropical, cyclical, and commutative. I also define a step logarithm function and express with it the bounds on quantum graph invariants in closed...