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Graphs with only caterpillars as spanning trees |
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| Authors: | Robert E Jamison Henry Martyn Mulder |
| Institution: | a Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975, USA b Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616-3793, USA c Econometrisch Instituut, Erasmus Universiteit, P.O. Box 1738, 3000 DR Rotterdam, Netherlands |
| Abstract: | A connected graph G is caterpillar-pure if each spanning tree of G is a caterpillar. The caterpillar-pure graphs are fully characterized. Loosely speaking they are strings or necklaces of so-called pearls, except for a number of small exceptional cases. An upper bound for the number of edges in terms of the order is given for caterpillar-pure graphs, and those which attain the upper bound are characterized. |
| Keywords: | Spanning tree Caterpillar |
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