<XML><RECORDS><RECORD><REFERENCE_TYPE>31</REFERENCE_TYPE><REFNUM>8204</REFNUM><AUTHORS><AUTHOR>Unsworth,C.</AUTHOR><AUTHOR>Prosser,P.</AUTHOR></AUTHORS><YEAR>2006</YEAR><TITLE>Rooted Tree and Spanning Tree Constraints</TITLE><PLACE_PUBLISHED>17th ECAI Workshop on Modelling and Solving Problems with Constraints</PLACE_PUBLISHED><PUBLISHER>N/A</PUBLISHER><LABEL>Unsworth:2006:8204</LABEL><KEYWORDS><KEYWORD>constraints graph connectivity tree rooted spanning</KEYWORD></KEYWORDS<ABSTRACT>We present two specialised constraints for modelling trees. The first constrains a set of variables, such that each variable takes as a value the index of its parent variable, with the exception of one variable that takes as a value its own index and becomes the root, and this results in a rooted tree. The second constraint assumes that constrained variables represent edges (or multi-edges) in a graph (or multi-graph). Edges may be selected or rejected by a search process, and the constraint ensures that this process results in a spanning tree. We also present a simple graph connectivity constraint and a no-cycle constraint.</ABSTRACT></RECORD></RECORDS></XML>