In this paper, we construct infinite families of tight regular tournaments. In particular, we prove that two classes of regular tournaments, tame molds and ample tournaments are tight. We exhibit an infinite family of 3-dichromatic tight tournaments. With this family we positively answer to one case of a conjecture posed by V. Neumann-Lara. Finally, we show that any tournament with a tight mold is also tight.
The dichromatic number dc(D) of a digraph D is defined to be the minimum number of colors such that the vertices of D can be colored in such a way that every chromatic class induces an acyclic subdigraph in D. The cyclic circulant tournament is denoted by [...] T=C→2n+1(1,2,…,n) , where V (T) = ℤ2n+1 and for every jump j ∈ 1, 2, . . . , n there exist the arcs (a, a + j) for every a ∈ ℤ2n+1. Consider the circulant tournament [...] C→2n+1〈k〉 obtained from the cyclic tournament by reversing one...
The mean value of the matching polynomial is computed in the family of all labeled graphs with n vertices. We introduce the dominating polynomial of a graph whose coefficients enumerate the dominating sets for a graph and study some properties of the polynomial. The mean value of this polynomial is determined in a certain special family of bipartite digraphs.
We study a particular digraph dynamical system, the so called digraph diclique operator. Dicliques have frequently appeared in the literature the last years in connection with the construction and analysis of different types of networks, for instance biochemical, neural, ecological, sociological and computer networks among others. Let be a reflexive digraph (or network). Consider and (not necessarily disjoint) nonempty subsets of vertices (or nodes) of . A disimplex of is the subdigraph...
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