General lower bound on the size of $$(H;k)$$ -stable graphs

Andrzej Żak ()
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Andrzej Żak: AGH University of Science and Technology

Journal of Combinatorial Optimization, 2015, vol. 29, issue 2, No 2, 367-372

Abstract: Abstract A graph $$G$$ is called $$(H;k)$$ -vertex stable if $$G$$ contains a subgraph isomorphic to $$H$$ ever after removing any $$k$$ of its vertices. By stab $$(H;k)$$ we denote the minimum size among the sizes of all $$(H;k)$$ -vertex stable graphs. In this paper we present a first (non-trivial) general lower bound for stab $$(H;k)$$ with regard to the order, connectivity and minimum degree of $$H$$ . This bound is nearly sharp for $$k=1$$ .

Keywords: Vertex-stable graph; Minimum degree; Connectivity (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10878-013-9595-y

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