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Browsing by Author "Nikodem, Mateusz"

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    Item type:Article, Access status: Open Access ,
    False alarms in fault-tolerant dominating sets in graphs
    (2012) Nikodem, Mateusz
    We develop the problem of fault-tolerant dominating sets (liar's dominating sets) in graphs. Namely, we consider a new kind of fault - a false alarm. Characterization of such fault-tolerant dominating sets in three different cases (dependent on the classification of the types of the faults) are presented.
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    On vertex stability of complete k-partite graphs
    (2015) Nikodem, Mateusz
    Let $H$ be any graph. We say that graph $G$ is $H$-stable if $G-u$ contains a subgraph isomorphic to $H$ for an arbitrary chosen $u\in V(G)$. We characterize all $H$-stable graphs of minimal size where $H$ is any complete $k$-partite graph. Thus, we generalize the results of Dudek and Żak regarding complete bipartite graphs.