Projects per year
Abstract
A set $\mathcal{S}$ of derangements (fixedpointfree permutations) of a set V generates a digraph with vertex set V and arcs $(x,x^{\,\sigma})$ for x V and $\sigma\in\mathcal{S}$. We address the problem of characterizing those infinite (simple loopless) digraphs which are generated by finite sets of derangements. The case of finite digraphs was addressed in an earlier work by the second and third authors. A criterion is given for derangement generation which resembles the criterion given by De Bruijn and Erdos for vertex colourings of graphs in that the property for an infinite digraph is determined by properties of its finite subdigraphs. The derangement generation property for a digraph is linked with the existence of a finite 1factor cover for an associated bipartite (undirected) graph.
Original language  English 

Pages (fromto)  961974 
Number of pages  14 
Journal  Quarterly Journal of Mathematics 
Volume  72 
Issue number  3 
DOIs  
Publication status  Published  1 Sep 2021 
Projects
 2 Finished

Edge decomposition of dense graphs
Australian Research Council (ARC)
30/06/17 → 29/06/22
Project: Research

Matchings in Combinatorial Structures
Wanless, I., Bryant, D. & Horsley, D.
Australian Research Council (ARC), Monash University, University of Queensland , University of Melbourne
1/01/15 → 10/10/20
Project: Research