$p$c阶不相交完全图的$k$-容错图$

IF 0.5 4区数学 Q3 MATHEMATICS

Discussiones Mathematicae Graph Theory Pub Date : 2022-12-13 DOI:10.7151/dmgt.2504

S. Cichacz, Agnieszka Gőrlich, Karol Suchan

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引用次数: 1

摘要

顶点容错是由Hayes~\cite{Hayes1976}于1976年提出的，从那时起，人们对它进行了不同方面的系统研究。在本文中，我们研究了$c$阶$p$不相交完全图的$k$-顶点容错图，即其中移除任何$k$顶点留下具有$c$级$p$非相交完全图作为子图的图。主要贡献是描述对于$k=1$、$p\geq1$和$c\geq3$具有尽可能少的边的图。此外，我们还分析了对于$k$的任何值，这种图的一些性质。

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

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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来源期刊

Discussiones Mathematicae Graph Theory MATHEMATICS-

CiteScore

2.20

自引率

0.00%

发文量

审稿时长

53 weeks

期刊介绍： The Discussiones Mathematicae Graph Theory publishes high-quality refereed original papers. Occasionally, very authoritative expository survey articles and notes of exceptional value can be published. The journal is mainly devoted to the following topics in Graph Theory: colourings, partitions (general colourings), hereditary properties, independence and domination, structures in graphs (sets, paths, cycles, etc.), local properties, products of graphs as well as graph algorithms related to these topics.