Full Orientability of the Square of a Cycle
Combinatorics
2012-02-28 v1
Abstract
Let D be an acyclic orientation of a simple graph G. An arc of D is called dependent if its reversal creates a directed cycle. Let d(D) denote the number of dependent arcs in D. Define m and M to be the minimum and the maximum number of d(D) over all acyclic orientations D of G. We call G fully orientable if G has an acyclic orientation with exactly k dependent arcs for every k satisfying m <= k <= M. In this paper, we prove that the square of a cycle C_n of length n is fully orientable except n=6.
Cite
@article{arxiv.1202.5721,
title = {Full Orientability of the Square of a Cycle},
author = {Fengwei Xu and Weifan Wang and Ko-Wei Lih},
journal= {arXiv preprint arXiv:1202.5721},
year = {2012}
}
Comments
7 pages, accepted by Ars Combinatoria on May 26, 2010