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Diskretn. Anal. Issled. Oper., 2013, Volume 20, Number 6, Pages 30–39 (Mi da751)  

This article is cited in 1 scientific paper (total in 1 paper)

On factorial subclasses of $K_{1,3}$-free graphs

V. A. Zamaraevab

a University of Nizhni Novgorod, 23 Gagarin Ave., 603950 Nizhni Novgorod, Russia
b National Research University Higher School of Economics, 136 Rodionov St., 603093 Nizhni Novgorod, Russia

Abstract: 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.

Full text: PDF file (257 kB)
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Bibliographic databases:
UDC: 519.1
Received: 23.10.2012
Revised: 09.03.2013

Citation: V. A. Zamaraev, “On factorial subclasses of $K_{1,3}$-free graphs”, Diskretn. Anal. Issled. Oper., 20:6 (2013), 30–39

Citation in format AMSBIB
\Bibitem{Zam13}
\by V.~A.~Zamaraev
\paper On factorial subclasses of $K_{1,3}$-free graphs
\jour Diskretn. Anal. Issled. Oper.
\yr 2013
\vol 20
\issue 6
\pages 30--39
\mathnet{http://mi.mathnet.ru/da751}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3185262}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. Lozin, V. Zamaraev, “The structure and the number of $P_7$-free bipartite graphs”, Eur. J. Comb., 65 (2017), 143–153  crossref  mathscinet  zmath  isi  scopus
  • Дискретный анализ и исследование операций
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