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arXiv · 2212.06892

$k$-fault-tolerant graphs for $p$ disjoint complete graphs of order $c$

Sylwia Cichacz·Agnieszka Görlich·Karol Suchan
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Abstract

Vertex-fault-tolerance was introduced by Hayes~\cite{Hayes1976} in 1976, and since then it has been systematically studied in different aspects. In this paper we study $k$-vertex-fault-tolerant graphs for $p$ disjoint complete graphs of order $c$, i.e., graphs in which removing any $k$ vertices leaves a graph that has $p$ disjoint complete graphs of order $c$ as a subgraph. The main contribution is to describe such graphs that have the smallest possible number of edges for $k=1$, $p \geq 1$, and $c \geq 3$. Moreover, we analyze some properties of such graphs for any value of $k$.

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Sylwia Cichacz, Agnieszka Görlich, Karol Suchan. 2022-12-13. $k$-fault-tolerant graphs for $p$ disjoint complete graphs of order $c$. https://doi.org/10.7151/dmgt.2504

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