This is the sequence of degrees of primitive groups which don’t synchronize a map of rank 3, equivalently graphs with clique number and chromatic number 3 having primitive automorphism groups. 72 more words

## Tags » Chromatic Number

#### An Experiment with Property-derived Invariants

We’ve coded a number of graph invariants and properties. One easy way to get more invariants is to use the characteristic functions of the properties we’ve already coded. 396 more words

#### Chromatic Number Upper Bound Conjectures

In our continued testing of the program we generated some conjectures for upper bounds for the chromatic number. We told the program the upper bounds due to… 138 more words

#### Chromatic Numbers and Distances in Finite Fields

A graph is a set of vertices and a set of edges so that some vertices are connected by edges. If a graph is simple… 515 more words

#### Concentration of the Chromatic Number

An interesting bound (problem from Rudi’s Modern coding theory book) regarding the chromatic number of a random graph. I first attempted it during the… 201 more words

#### Lecture 6: Borsuk-Ulam and some combinatorial applications

Now we’ll move away from spectral methods, and into a few lectures on topological methods. Today we’ll look at the Borsuk-Ulam theorem, and see a stunning application to combinatorics, given by… 1,341 more words