Abstract
It is well known that a graph is outerplanar if and only if it is K4-minor free and K2,3-minor free. Campos and Wakabayashi (2013) recently proved that γ(G)≤⌊n+k4⌋ for any maximal outerplanar graph G of order n≥3 with k vertices of degree 2, where γ(G) denotes the domination number of G. Tokunaga (2013) provided a short proof for the above theorem. Based on some structural properties of K2,3-minor free graphs and K4-minor free graphs, applying the idea of Tokunaga we extend the theorem of Campos and Wakabayashi to all maximal K4-minor free graphs and all maximal K2,3-minor free graphs. We also disprove two conjectures of Tokunaga on planar graphs.
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