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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TIMB_2007_15_1_a9,
     author = {T. V. Lubasheva and Yu. M. Metelsky},
     title = {Characterization of the graphs with bounded above equivalence partition number in the class of $\mathcal U$-split graphs},
     journal = {Trudy Instituta matematiki},
     pages = {91--97},
     publisher = {mathdoc},
     volume = {15},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2007_15_1_a9/}
}
TY  - JOUR
AU  - T. V. Lubasheva
AU  - Yu. M. Metelsky
TI  - Characterization of the graphs with bounded above equivalence partition number in the class of $\mathcal U$-split graphs
JO  - Trudy Instituta matematiki
PY  - 2007
SP  - 91
EP  - 97
VL  - 15
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMB_2007_15_1_a9/
LA  - ru
ID  - TIMB_2007_15_1_a9
ER  - 
%0 Journal Article
%A T. V. Lubasheva
%A Yu. M. Metelsky
%T Characterization of the graphs with bounded above equivalence partition number in the class of $\mathcal U$-split graphs
%J Trudy Instituta matematiki
%D 2007
%P 91-97
%V 15
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMB_2007_15_1_a9/
%G ru
%F TIMB_2007_15_1_a9
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/