Csilla Bujtas: Bipartite graphs with close domination and k-domination numbers

Tuesday, January 12th at 10.15

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Meeting ID: 952 0306 8752
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Abstract. Let k be a positive integer and let G be a graph with vertex set V(G). A subset D \subseteq V(G) is a k-dominating set if every vertex outside D is adjacent to at least k vertices in D. The k-domination number \gamma_k(G) is the minimum cardinality of a k-dominating set in G. For any graph G, we know that  \gamma_k(G) >= \gamma(G)+k-2 where \Delta(G) >= k >= 2  and this bound is sharp for every  k >=  2. In the talk, after discussing some prliminaries, we characterize bipartite graphs satisfying the equality for  k >= 3 and present a necessary and sufficient condition for a bipartite graph to satisfy the equality hereditarily when  k=3. We also prove that the problem of deciding whether a graph satisfies the given equality is NP-hard in general.

Based on a joint work with Gülnaz Boruzanli Ekinci.