# A short construction of highly chromatic digraphs without short cycles

## Document Type

Presentation Abstract

## Presentation Date

5-5-2014

## Abstract

A natural digraph analogue of the graph-theoretic concept of an 'independent set' is that of an 'acyclic set', namely a set of vertices not spanning a directed cycle. Hence a digraph analogue of a graph coloring is a decomposition of the vertex set into acyclic sets. In the spirit of a famous theorem of P. Erdős [Graph theory and probability, Canad. J. Math., **11**:34-38, (1959)], it was shown probabilistically in [D. Bokal et al., The circular chromatic number of a digraph, J. Graph Theory, **46**(3): 227-240, 2004] that there exist digraphs with arbitrarily large girth and chromatic number. Here I give a construction of such digraphs.

## Recommended Citation

Severino, Michael, "A short construction of highly chromatic digraphs without short cycles" (2014). *Colloquia of the Department of Mathematical Sciences*. 451.

https://scholarworks.umt.edu/mathcolloquia/451

## Additional Details

Monday, May 5, 2014 at 3:10 p.m. in Math 103

4:00 p.m. Refreshments in Math Lounge 109