Examples of using Its complement in English and their translations into Russian
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Official
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Colloquial
A 2-design and its complement have the same order.
If a graph has a skew partition,so does its complement.
Its complement, the 10-regular Clebsch graph, is also a strongly regular graph.
If G{\displaystyle G}is disconnected, its complement is connected.
There are only two connected graphs that are 4-ultrahomogeneous but not 5-ultrahomogeneous:the Schläfli graph and its complement.
A set is independent if and only if its complement is a vertex cover.
Near the protected area there is a large medieval Royal Castle anda beautiful park as its complement.
A graph G is a Berge graph if neither G nor its complement contains an induced cycle of odd length 5 or more.
Nikiforov(2005) uses Turán graphs to supply a lower bound for the sum of the kth eigenvalues of a graph and its complement.
Connected components of a graph G{\displaystyle G}, or of its complement graph are also modules of G{\displaystyle G.
The first of these two theorems was the perfect graph theorem of Lovász(1972),stating that a graph is perfect if and only if its complement is perfect.
Ramsey's theorem states that every graph or its complement graph contains a clique with at least a logarithmic number of vertices.
A strongly regular graph is called primitive if both the graph and its complement are connected.
The trefoil is a fibered knot,meaning that its complement in S 3{\displaystyle S^{3}} is a fiber bundle over the circle S 1{\displaystyle S^{1.
The Paley graph of order 101 is currently the largest known graph G such that neither G nor its complement contains a complete 6-vertex subgraph.
Its complement is a specific approach that involves the conception and application of positive measures in favour of women with a view to establishing de facto equality between men and women.
The bourgeois family will vanish as a matter of course when its complement vanishes, and both will vanish with the vanishing of capital.
In this version each edge has a real number, its weight, and the objective is to maximize not the number of edges butthe total weight of the edges between S and its complement.
A graph G is a permutation graph if andonly if both G and its complement G¯{\displaystyle{\overline{G}}} are comparability graphs.
It is an elementary geometry to see that the complex tangent space to C P n{\displaystyle\mathbb{C}\mathbb{P}^{n}}at the point L is naturally the set of linear maps from L to its complement.
The Paley graph of order 17 is the unique largest graph G such that neither G nor its complement contains a complete 4-vertex subgraph Evans et al. 1981.
A graph is perfect if and only if its complement is perfect, and Kőnig's theorem can be seen as equivalent to the statement that the complement of a bipartite graph is perfect.
Since trapezoid graphs are a subset of co-comparability graphs, if G{\displaystyle{G}}is a trapezoid graph, its complement G′{\displaystyle{G'}} must be a comparability graph.
That is, for every 17-vertex graph G, either G or its complement contains W6 as a subgraph, while neither the 17-vertex Paley graph nor its complement contains a copy of K4.
Denote the Ramsey number of two triangular books by r( B p, B q).{\displaystyle r(B_{p},\ B_{q}).} This is the smallest number r{\displaystyle r} such that for every r{\displaystyle r}-vertex graph, either the graph itself contains B p{\displaystyle B_{p}} as a subgraph,or its complement graph contains B q{\displaystyle B_{q}} as a subgraph.
Improvement of the model was its complement condition identical control stations located in several transmissions ranges conditions and a decomposition representation connected mesh-network.
As part of the trio was a long term partner Ganelina bassist Victor Fonarev, who came to the festival from the United States and drummer Klaus Kugel,and a quartet of its complement trumpeter Sergei Pron- and debutant Israel, a leading trumpeter and, in my opinion, the main character of the festival.
C is a minimal vertex cover if and only if its complement I is a maximal independent set, and C is a minimum vertex cover if and only if its complement is a maximum independent set.
Claude Berge had conjectured in the early 1960s that perfect graphs were the sameas the Berge graphs, graphs with no induced odd cycle(of length five or more) or its complement, and(because cycles and their complements do not have skew partitions) no minimal non-Berge graph can have a skew partition.
Hayward(1985) showed, analogously, that every connected and co-connected weakly chordal graph(a graph with no induced cycle or its complement of length greater than four) with four ormore vertices has a star cutset or its complement, from which it follows by Chvátal's lemma that every such graph is perfect.