From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3682 Path: news.gmane.org!not-for-mail From: John Stell Newsgroups: gmane.science.mathematics.categories Subject: relations on graphs Date: Thu, 8 Mar 2007 15:15:57 +0000 (GMT) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: ger.gmane.org 1241019453 9763 80.91.229.2 (29 Apr 2009 15:37:33 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:37:33 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Thu Mar 8 17:01:59 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 08 Mar 2007 17:01:59 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HPPar-0001xU-TS for categories-list@mta.ca; Thu, 08 Mar 2007 16:52:09 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 36 Original-Lines: 21 Xref: news.gmane.org gmane.science.mathematics.categories:3682 Archived-At: For a set, X, relations on X are equivalent to join-preserving functions on the powerset P(X). If we replace X by a graph, the usual notion of a relation on a graph is a pair of relations one on edges and one on nodes subject to an obvious compatibility condition. However such relations are not as general as the join-preserving functions on the bi-Heyting algebra of subgraphs (consider for example the one node, one edge graph). If we mean relations in this more general sense could there be a notion of converse? (anything for which R** = R, and 1* = 1, and (RS)* = S*R*) Is there any literature which discusses different possible notions for relations on graphs? John Stell