Null-homotopic graphs and triangle-completions of spanning trees

Rautenbach, Dieter GND; Schäfer, Philipp Matthias

We prove that a connected graph whose cycle space is generated by its triangles and which is either planar or of maximum degree at most four has the property that it arises from an arbitrary spanning tree by iteratively adding edges which complete triangles.

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Rautenbach, Dieter / Schäfer, Philipp Matthias: Null-homotopic graphs and triangle-completions of spanning trees. 2009.

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