Trees with proper thinness 2
Keywords:
trees, proper thinness, characterizationsAbstract
The proper thinness of a graph is an invariant that generalizes the concept of a proper interval graph. Every graph has a numerical value of proper thinness and the graphs with proper thinness 1 are exactly the proper interval graphs. In this work we focus on the calculation of proper thinness for trees. We characterize trees of proper thinness 2, both structurally and by their minimal forbidden induced subgraphs. We also show why the results obtained for trees of proper thinness 2 cannot be generalized to trees of proper thinness 3.
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Copyright (c) 2025 Flavia Bonomo-Braberman, Ignacio Maqueda, Nina Pardal
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