The Dn,m (r, c)-digraphs are closely related to the proximity graphs of Jaromczyk and Toussaint (1992) and might be considered as a special case of covering sets of Tuza (1994) and intersection digraphs of Sen et al. (1989).
The Distribution of the Domination Number of a Family of Random Interval Catch Digraphs
In , Caro, Lev, Roditty, Tuza and Yuster investigated the extremal graph-theoretic behavior of rainbow connection number.
Rainbow connections of graphs -- A survey
In , Caro, Lev, Roditty, Tuza and Yuster also derived a result which gives an upper bound for rainbow connection number according to the order and the number of vertexdisjoint cycles.
Rainbow connections of graphs -- A survey
For example, in Caro, Lev, Roditty, Tuza and Yuster derived Theorem 2.23 according to the ear-decomposition of a 2-connected graph.
Rainbow connections of graphs -- A survey
In , Caro, Lev, Roditty, Tuza and Yuster investigated the graphs with small rainbow connection numbers, and they gave a suﬃcient condition that guarantees rc(G) = 2.
Rainbow connections of graphs -- A survey
This substantially generalizes a result due to Caro, Lev, Roditty, Tuza and Yuster (see Theorem 2.46).
Rainbow connections of graphs -- A survey
At the end of , Caro, Lev, Roditty, Tuza and Yuster gave two conjectures (see Conjecture 4.1 and Conjecture 4.2 in ) on the complexity of determining the rainbow connection numbers of graphs.
Rainbow connections of graphs -- A survey
Tuza, Radius, diameter , and minimum degree, J.
Rainbow connections of graphs -- A survey
Tuza, F inding optimal rainbow connection is hard, Preprint 2009.
Rainbow connections of graphs -- A survey
We remark that a well known conjecture of Tuza states that the upper bound can be improved to ν (G) ≤ 2τ (G).
Testing perfection is hard
The Erd˝os-Ko-Rado theorem tells us how large an intersecting family of r-sets from an n-set can be, while results due to Lov´asz and Tuza give bounds on the number of singletons that can occur as pairwise intersections of sets from such a family.
The number of k-intersections of an intersecting family of r-sets
Theorem 2 was subsequently improved by Tuza who gave the following bounds for α(r) .
The number of k-intersections of an intersecting family of r-sets
Tuza, Critical hypergraphs and intersecting set-pair systems, J.
The number of k-intersections of an intersecting family of r-sets
Tuza, Applications of the set-pair method in extremal hypergraphs, in: P.
The number of k-intersections of an intersecting family of r-sets
Manoussakis, Spyratos, Tuza and Voigt proved the next result.
Properly Coloured Cycles and Paths: Results and Open Problems
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