Analytic colorings

Measurable 3-colorings of Acyclic Graphs

This is the first of two lectures on measurable chromatic numbers given in June 2010 at the University of Barcelona. Our main result here is that acyclic locally finite analytic graphs on Polish spaces admit Baire measurable 3-colorings.

Baire-class ξ colorings: the first three levels

The G0-dichotomy due to Kechris, Solecki and Todorčević characterizes the analytic relations having a Borel-measurable countable coloring. We give a version of the G0-dichotomy for Σ 0 ξ-measurable countable colorings when ξ ≤ 3. A Σ 0 ξ-measurable countable coloring gives a covering of the diagonal consisting of countably many Σξ squares. This leads to the study of countable unions of Σξ recta...

Perfect $2$-colorings of the Platonic graphs

In this paper, we enumerate the parameter matrices of all perfect $2$-colorings of the Platonic graphs consisting of the tetrahedral graph, the cubical graph, the octahedral graph, the dodecahedral graph, and  the icosahedral graph.

On the Defining Number of (2n - 2)-Vertex Colorings of Kn x Kn

A Combinatorial Proof of Sun's \Curious" Identity

A binomial coeÆcient identity due to Zhi-Wei Sun is the subject of half a dozen recent papers that prove it by various analytic techniques and establish a generalization. Here we give a simple proof that uses weight-reversing involutions on suitable con gurations involving dominos and colorings. With somewhat more work, the method extends to the generalization also. 0 Introduction The identity