Nice labeling problem for event structures: a counterexample
Combinatorics
2015-03-17 v1
Abstract
In this note, we present a counterexample to a conjecture of Rozoy and Thiagarajan from 1991 (called also the nice labeling problem) asserting that any (coherent) event structure with finite degree admits a labeling with a finite number of labels, or equivalently, that there exists a function such that an event structure with degree admits a labeling with at most labels. Our counterexample is based on the Burling's construction from 1965 of 3-dimensional box hypergraphs with clique number 2 and arbitrarily large chromatic numbers and the bijection between domains of event structures and median graphs established by Barth\'elemy and Constantin in 1993.
Cite
@article{arxiv.1107.1207,
title = {Nice labeling problem for event structures: a counterexample},
author = {Victor Chepoi},
journal= {arXiv preprint arXiv:1107.1207},
year = {2015}
}