Geodesic
On factorial subclasses of $K_{1,3}$-free graphs
Diskretnyj analiz i issledovanie operacij, Tome 20 (2013) no. 6, pp. 30-39

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For a set of labeled graphs $X$, let $X_n$ be the set of $n$-vertex graphs from $X$. A hereditary class $X$ is called at most factorial if there exist positive constants $c$ and $n_0$ such that $|X_n|\leq n^{cn}$ for all $n>n_0$. Lozin's conjecture states that a hereditary class $X$ is at most factorial if and only if each of the following three classes is at most factorial: $X\cap B$, $X\cap\widetilde B$ and $X\cap S$, where $B,\widetilde B$ and $S$ are the classes of bipartite, co-bipartite and split graphs respectively. We prove this conjecture for subclasses of $K_{1,3}$-free graphs defined by two forbidden subgraphs. Bibliogr. 10.
Keywords: hereditary class of graphs, factorial class. 
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     author = {V. A. Zamaraev},
     title = {On factorial subclasses of $K_{1,3}$-free graphs},
     journal = {Diskretnyj analiz i issledovanie operacij},
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     publisher = {mathdoc},
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     number = {6},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2013_20_6_a2/}
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V. A. Zamaraev. On factorial subclasses of $K_{1,3}$-free graphs. Diskretnyj analiz i issledovanie operacij, Tome 20 (2013) no. 6, pp. 30-39. http://geodesic.mathdoc.fr/item/DA_2013_20_6_a2/