Abstract
We establish that for any connected graph G of order \(n \ge 6\), a minimum vertex-edge dominating set of G has at most n/3 vertices, thus affirmatively answering the open question posed by Boutrig et al. (Aequ Math 90(2):355–366, 2016).
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I would like to show my gratitude to Jerzy Topp for sharing his pearls of wisdom during several hours of our inspiring discussions.
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Supported by the Grant 2015/17/B/ST6/01887 (National Science Centre, Poland).
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Żyliński, P. Vertex-edge domination in graphs. Aequat. Math. 93, 735–742 (2019). https://doi.org/10.1007/s00010-018-0609-9
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DOI: https://doi.org/10.1007/s00010-018-0609-9