The Brooks Periodical Comet

The Polanyi Society Periodical

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

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...

Of Recent Periodical Literature

The demography of Sandwich in this period has attracted attention from previous historians but has not been systematically studied. This article goes some way towards rectifying this situation by tracing the town’s growth from c. 1,500–1,700 in the mid-sixteenth century to c. 5,500 by 1610, population growth ending during the 1630s after which decline set in, the 1671 Hearth Tax suggesting a po...