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On Double Domination in Graphs
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
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.
Nonrepetitive vertex colorings of graphs
On Dominating Sets and Independent Sets of Graphs
- J. Harant, Anja Pruchnewski, M. Voigt
- MathematicsCombinatorics, Probability and Computing
- 1 November 1999
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
- MathematicsDiscuss. Math. Graph Theory
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
On cycles through specified vertices
Non-hamiltonian 4/5-tough maximal planar graphs
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 ScienceDiscret. Math.
- 28 June 1998