NDLI: A Note on a Question of C. D. Savage

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Naatz, Michael
Copyright Year	2001
Abstract	Given a graph G and an orientation $\sigma$ of some of its edges, consider the graph $AO_\sigma(G)$ which is defined as follows: The vertices are the acyclic orientations of G which agree with $\sigma$, and two of these are adjacent if they differ only by the reversal of a single edge. $AO_\sigma(G)$ is easily seen to be bipartite. The purpose of this note is to show that it need not contain a Hamilton path even if both partite sets have the same cardinality. This answers a question of C. D. Savage [SIAM Rev., 39 (1997), pp. 605--629] and sheds new light onto two well-known open questions in the field of combinatorial Gray codes.
Starting Page	116
Ending Page	120
Page Count	5
File Format	PDF
ISSN	08954801
DOI	10.1137/S0895480100369195
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	1
Volume Number	14
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-01
Access Restriction	Subscribed
Subject Keyword	Enumeration in graph theory adjacent transposition Combinatorics of partially ordered sets Hamilton path Hamilton cycle Directed graphs (digraphs), tournaments Eulerian and Hamiltonian graphs linear extension acyclic orientation poset
Content Type	Text
Resource Type	Article
Subject	Mathematics

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A Note on a Question of C. D. Savage