Geodesic
Characterization of the graphs with bounded above equivalence partition number in the class of $\mathcal U$-split graphs
Trudy Instituta matematiki, Tome 15 (2007) no. 1, pp. 91-97.

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It is proved that, for an arbitrary fixed $k\ge3$, the class $L^l(k)$ of graphs with equivalence partition number at most $k$ can be characterized by means of a finite list of forbidden induced subgraphs in an extension of the class of split graphs — the class of $\mathcal{U}$-split graphs. In the case $k=3$ the corresponding list as well as a description of the graphs in $L^l(3)$ in the class of $\mathcal{U}$-split graphs not being split are obtained. 
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T. V. Lubasheva; Yu. M. Metelsky. Characterization of the graphs with bounded above equivalence partition number in the class of $\mathcal U$-split graphs. Trudy Instituta matematiki, Tome 15 (2007) no. 1, pp. 91-97. http://geodesic.mathdoc.fr/item/TIMB_2007_15_1_a9/

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