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- Miklós Biró, Mihály Hujter, Zsolt Tuza
- Discrete Mathematics
- 1992

of the following general problem on vertex colorings of graphs. Suppose that some vertices of a graph G are assigned to some colors. Can this precoloring be extended to a proper coloring of G with at most k colors (for some given k)? This question was motivated by practical problems in scheduling and VLSI theory. Here we investigate its complexity status… (More)

- Jan Kratochvíl, Petr Savický, Zsolt Tuza
- SIAM J. Comput.
- 1993

- Yair Caro, Arieh Lev, Yehuda Roditty, Zsolt Tuza, Raphael Yuster
- Electr. J. Comb.
- 2008

An edge-colored graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph G, denoted rc(G), is the smallest number of colors that are needed in order to make G rainbow connected. In this paper we prove several non-trivial upper bounds for rc(G), as well as… (More)

- L. Kászonyi, Zsolt Tuza
- Journal of Graph Theory
- 1986

Let F = {F,, . . .} be a given class of forbidden graphs. A graph G is called F-saturated if no F, E F is a subgraph of G but the addition of an arbitrary new edge gives a forbidden subgraph. In this paper the minimal number of edges in F-saturated graphs is examined. General estimations are given and the structure of minimal graphs is described for some… (More)

- Svatopluk Poljak, Zsolt Tuza
- Combinatorial Optimization
- 1993

- Yair Caro, Zsolt Tuza
- Journal of Graph Theory
- 1991

A vertex set Y in a (hyperbraph is called k-independent if in the sub(hyper)graph induced by Y every vertex is incident to less than k edges. We prove a lower bound for the maximum cardinality of a k-independent set-in terms of degree sequences-which strengthens and generalizes several previously known results, including Turin's theorem.

- Hans Kellerer, Vladimir Kotov, Maria Grazia Speranza, Zsolt Tuza
- Oper. Res. Lett.
- 1997

- Noga Alon, Zsolt Tuza, Margit Voigt
- Discrete Mathematics
- 1997

A graph G is (a, b)-choosable if for any assignment of a list of a colors to each of its vertices there is a subset of b colors of each list so that subsets corresponding to adjacent vertices are disjoint. It is shown that for every graph G, the minimum ratio a/b where a, b range over all pairs of integers for which G is (a, b)-choosable is equal to the… (More)

- Jan Kratochvíl, Zsolt Tuza, Margit Voigt
- WG
- 2002

Computing the chromatic number of a graph is an NP-hard problem. For random graphs and some other classes of graphs, estimators of the expected chromatic number have been well studied. In this paper, a new 0–1 integer programming formulation for the graph coloring problem is presented. The proposed new formulation is used to develop a method that generates… (More)