Monochromatic kernel-perfectness of special classes of digraphs

Hortensia Galeana-Sánchez; Luis Alberto Jiménez Ramírez

Displaying similar documents to “Monochromatic kernel-perfectness of special classes of digraphs”

On a problem of E. Prisner concerning the biclique operator

Bohdan Zelinka (2002)

Mathematica Bohemica

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The symbol $K (B, C)$ denotes a directed graph with the vertex set $B \cup C$ for two (not necessarily disjoint) vertex sets $B, C$ in which an arc goes from each vertex of $B$ into each vertex of $C$ . A subdigraph of a digraph $D$ which has this form is called a bisimplex in $D$ . A biclique in $D$ is a bisimplex in $D$ which is not a proper subgraph of any other and in which $B \neq \emptyset$ and $C \neq \emptyset$ . The biclique digraph $\vec{C} (D)$ of $D$ is the digraph whose vertex set is the set of all bicliques in $D$ and in which there is an arc from $K (B_{1}, C_{1})$ into $K (B_{2}, C_{2})$ ...

The classification of finite groups by using iteration digraphs

Uzma Ahmad, Muqadas Moeen (2016)

Czechoslovak Mathematical Journal

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A digraph is associated with a finite group by utilizing the power map $f : G \to G$ defined by $f (x) = x^{k}$ for all $x \in G$ , where $k$ is a fixed natural number. It is denoted by $γ_{G} (n, k)$ . In this paper, the generalized quaternion and $2$ -groups are studied. The height structure is discussed for the generalized quaternion. The necessary and sufficient conditions on a power digraph of a $2$ -group are determined for a $2$ -group to be a generalized quaternion group. Further, the classification of two generated $2$ -groups as abelian...

Signed domination and signed domatic numbers of digraphs

Lutz Volkmann (2011)

Discussiones Mathematicae Graph Theory

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Let D be a finite and simple digraph with the vertex set V(D), and let f:V(D) → -1,1 be a two-valued function. If $\sum_{x \in N ¯ [v]} f (x) \geq 1$ for each v ∈ V(D), where N¯[v] consists of v and all vertices of D from which arcs go into v, then f is a signed dominating function on D. The sum f(V(D)) is called the weight w(f) of f. The minimum of weights w(f), taken over all signed dominating functions f on D, is the signed domination number $γ_{S} (D)$ of D. A set $f ₁, f ₂, . . ., f_{d}$ of signed dominating functions on D with the property that...

Decompositions of nearly complete digraphs into t isomorphic parts

Mariusz Meszka, Zdzisław Skupień (2009)

Discussiones Mathematicae Graph Theory

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An arc decomposition of the complete digraph Kₙ into t isomorphic subdigraphs is generalized to the case where the numerical divisibility condition is not satisfied. Two sets of nearly tth parts are constructively proved to be nonempty. These are the floor tth class ( Kₙ-R)/t and the ceiling tth class ( Kₙ+S)/t, where R and S comprise (possibly copies of) arcs whose number is the smallest possible. The existence of cyclically 1-generated decompositions of Kₙ into cycles $^{\to} C_{n - 1}$ and into paths...

Self-diclique circulant digraphs

Marietjie Frick, Bernardo Llano, Rita Zuazua (2015)

Mathematica Bohemica

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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 $D = (V, A)$ be a reflexive digraph (or network). Consider $X$ and $Y$ (not necessarily disjoint) nonempty subsets of vertices (or nodes) of $D$ . A disimplex $K (X, Y)$ of $D$ is...

A note on perfect matchings in uniform hypergraphs with large minimum collective degree

Vojtěch Rödl, Andrzej Ruciński, Mathias Schacht, Endre Szemerédi (2008)

Commentationes Mathematicae Universitatis Carolinae

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For an integer $k \geq 2$ and a $k$ -uniform hypergraph $H$ , let $δ_{k - 1} (H)$ be the largest integer $d$ such that every $(k - 1)$ -element set of vertices of $H$ belongs to at least $d$ edges of $H$ . Further, let $t (k, n)$ be the smallest integer $t$ such that every $k$ -uniform hypergraph on $n$ vertices and with $δ_{k - 1} (H) \geq t$ contains a perfect matching. The parameter $t (k, n)$ has been completely determined for all $k$ and large $n$ divisible by $k$ by Rödl, Ruci’nski, and Szemerédi in [, submitted]. The values of $t (k, n)$ are very close to $n / 2 - k$ . In fact, the function $t (k, n) = n / 2 - k + c_{n, k}$ ,...

Possibly there is no uniformly completely Ramsey null set of size $2^{ω}$

Andrzej Nowik (2002)

Colloquium Mathematicae

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We show that under the axiom $C P A_{c u b e}$ there is no uniformly completely Ramsey null set of size $2^{ω}$ . In particular, this holds in the iterated perfect set model. This answers a question of U. Darji.

Less than $2^{ω}$ many translates of a compact nullset may cover the real line

Márton Elekes, Juris Steprāns (2004)

Fundamenta Mathematicae

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We answer a question of Darji and Keleti by proving that there exists a compact set C₀ ⊂ ℝ of measure zero such that for every perfect set P ⊂ ℝ there exists x ∈ ℝ such that (C₀+x) ∩ P is uncountable. Using this C₀ we answer a question of Gruenhage by showing that it is consistent with ZFC (as it follows e.g. from $c o f () < 2^{ω}$ ) that less than $2^{ω}$ many translates of a compact set of measure zero can cover ℝ.