Victor Zamaraev

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For a graph property X, let Xn be the number of graphs with vertex set {1, . . . , n} having property X, also known as the speed of X. A property X is called factorial if X is hereditary (i.e. closed under taking induced subgraphs) and n1 ≤ Xn ≤ n c2n for some positive constants c1 and c2. Hereditary properties with the speed slower than factorial are(More)
The notion of augmenting graphs generalizes Berge’s idea of augmenting chains, which was used by Edmonds in his celebrated solution of the maximum matching problem. This problem is a special case of the more general maximum independent set (MIS) problem. Recently, the augmenting graph approach has been successfully applied to solve MIS in various other(More)
An induced matching M in a graph G is dominating if every edge not in M shares exactly one vertex with an edge in M . The dominating induced matching problem (also known as efficient edge domination) asks whether a graph G contains a dominating induced matching. This problem is generally NP-complete, but polynomial-time solvable for graphs with some special(More)
An upper dominating set in a graph is a minimal (with respect to set inclusion) dominating set of maximum cardinality. The problem of finding an upper dominating set is generally NP-hard, but can be solved in polynomial time in some restricted graph classes, such as P4-free graphs or 2K2-free graphs. For classes defined by finitely many forbidden induced(More)
Clique-width is an important graph parameter due to its algorithmic and structural properties. A graph class is hereditary if it can be characterized by a (not necessarily finite) set H of forbidden induced subgraphs. We initiate a systematic study into the boundedness of clique-width of hereditary graph classes closed under complementation. First, we(More)
Corrigendum Corrigendum to ‘‘Locally bounded coverings and factorial properties of graphs’’ [European J. Combin. 33 (2012) 534–543] Vadim V. Lozin a, Colin Mayhill b, Victor Zamaraev c,d a DIMAP and Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK bMathematics Institute, University of Warwick, Coventry CV4 7AL, UK c National Research(More)