Mr. Brooks on Poetry

An Improvement on Brooks’ Theorem

We prove that χ(G) ≤ max { ω(G),∆2(G), 5 6 (∆(G) + 1) } for every graph G with ∆(G) ≥ 3. Here ∆2 is the parameter introduced by Stacho that gives the largest degree that a vertex v can have subject to the condition that v is adjacent to a vertex whose degree is at least as large as its own. This upper bound generalizes both Brooks’ Theorem and the Ore-degree version of Brooks’ Theorem.

On Poetry and Mind

Pottery, Poetry, and Prophecy: An Essay on Biblical Poetry

OETRY is not only central in the title, but for the study of the Hebrew Bible. There is no intention here of disvaluing the prose of the Bible, which constitutes the first major literary composition in that medium ever produced, so far as I am aware, whether we speak of the so-called Court History and the J source of the Pentateuch of the 10th century B.C., or the composite whole which we may c...

On Brooks' Theorem for Sparse Graphs

Let G be a graph with maximum degree ∆(G). In this paper we prove that if the girth g(G) of G is greater than 4 then its chromatic number, χ(G), satisfies χ(G) ≤ (1 + o(1)) ∆(G) log ∆(G) where o(1) goes to zero as ∆(G) goes to infinity. (Our logarithms are base e.) More generally, we prove the same bound for the list-chromatic (or choice) number: χ l (G) ≤ (1 + o(1)) ∆(G) log ∆(G) provided g(G)...

On stratification in poetry

Texts are composed of many different strata on different levels. A method is proposed to find the number of strata at the word-form level in Slovak poetry and to study the relationship between the parameters of the fitting function.