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Regular version of the site

Article

Almost all factorial subclasses of quasi-line graphs with respect to one forbidden subgraph

Moscow Journal of Combinatorics and Number Theory. 2011. Vol. 1. No. 3. P. 277-286.
Zamaraev V. A.

For a graph property X, let Xn be the set of graphs with the vertex set  {1, . . . , n} that satisfy the property X. A property X is called factorial if X is hereditary (i. e. closed under taking induced subgraphs) and nc1n ≤ X ≤ nc2n for some positive constants c1 and c2. A graph G is a quasi-line if for every vertex v, the set of neighbors of v can be expressed as a union of two cliques. In the present paper we identify almost all factorial subclasses of quasi-line graphs defined by one forbidden induced subgraph. We use these new results to prove that the class Free(K1,3,W4) is factorial, which improves on a result of Lozin, Mayhill and Zamaraev [8].