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On Double Domination in Graphs
TLDR
If G has order n with minimum degree ‐ and average degree d, then ∞£2(G) • ((ln(1 + d) + ln‐ + 1)=‐)n, where the minimum is taken over the n-dimensional cube C n.
On Domination in Graphs
TLDR
It is proved that their optimum values equal the domination number γ of G, and an efficient approximation method is developed and known upper bounds on γ are slightly improved.
On Dominating Sets and Independent Sets of Graphs
TLDR
The approach yields an improvement of an upper bound for the domination number found by N. Alon and J. H. Spencer, and it is proved that γk(G) = min fk(p), where the minimum is taken over the n-dimensional cube Cn.
Some news about the independence number of a graph
  • J. Harant
  • Mathematics
    Discuss. Math. Graph Theory
  • 2000
For a finite undirected graph G on n vertices some continuous optimization problems taken over the n-dimensional cube are presented and it is proved that their optimum values equal the independence
On the radius of graphs
Menger's Theorem
TLDR
A short and elementary proof of a more general theorem is given of Menger's Theorem for digraphs, which states that for any two vertex sets A and B of a digraph D such that A cannot be separated from B by a set of at most t vertices, there are t + 1 disjoint A-B- paths in D.
A lower bound on the independence number of a graph
  • J. Harant
  • Mathematics, Computer Science
    Discret. Math.
  • 28 June 1998
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