# An Exact Enumeration of Distance-Hereditary Graphs

@article{Chauve2017AnEE, title={An Exact Enumeration of Distance-Hereditary Graphs}, author={C{\'e}dric Chauve and {\'E}ric Fusy and J{\'e}r{\'e}mie O. Lumbroso}, journal={ArXiv}, year={2017}, volume={abs/1608.01464} }

Distance-hereditary graphs form an important class of graphs, from the theoretical point of view, due to the fact that they are the totally decomposable graphs for the split-decomposition. The previous best enumerative result for these graphs is from Nakano et al. (J. Comp. Sci. Tech., 2007), who have proven that the number of distance-hereditary graphs on $n$ vertices is bounded by ${2^{\lceil 3.59n\rceil}}$.
In this paper, using classical tools of enumerative combinatorics, we improve on…

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