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Kanten-kritische graphen mit der zusammenhangszahl 2
Authors:Walter Wessel Dipl-Math
Institution:(1) Institut für Reine Mathematik, Deutsche Akademie der Wissenschaften zu Berlin, Rudower Chaussee 5, 1199 Berlin
Abstract:A set oS of vertices of a graph G represents G if each edge of G is incident with at least one vertex of oS. A graph G is said to be edge-critical if the minimal number of vertices necessary to represent G decreases if any edge of G is omitted. Plummer 5] has given a method to construct an infinite family of edge-critical graphs with connectivity number 2. We use this method to construct a more extensive class of edge-critical graphs with connectivity number 2 and show that all edge-critical graphs with this connectivity number (neK2) can be constructed from ldquosmallerrdquo edge-critical graphs. Finally we give examples of edge-critical graphs not constructable from smaller ones by this method.
Keywords:
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