José D. Alvarado

activity

20152023

2

-rainbow domination to weak Roman domination

1 citations · 2 across the 6 of their papers we have counts for

collaborators

8 papers

math.CO2023

Moderate deviations of triangle counts in sparse Erdős-Rényi random graphs $G (n, m)$ and $G (n, p)$

José D. Alvarado, Leonardo Gonçalves de Oliveira, Simon Griffiths

We consider the question of determining the probability of triangle count deviations in the Erdős-Rényi random graphs $G (n, m)$ and $G (n, p)$ with densities larger than $n^{-1/2}(\lo…

math.CO2018

On the maximum number of minimum dominating sets in forests

J. D. Alvarado, S. Dantas, E. Mohr +1

Fricke, Hedetniemi, Hedetniemi, and Hutson asked whether every tree with domination number $γ$ has at most $2^{γ}$ minimum dominating sets. Bien gave a counterexample, which allows t…

math.CO2017

Sandwiches Missing Two Ingredients of Order Four

José D. Alvarado, Simone Dantas, Dieter Rautenbach

For a set $F$ of graphs, an instance of the $F$ -{\sc free Sandwich Problem} is a pair $(G_{1}, G_{2})$ consisting of two graphs $G_{1}$ and $G_{2}$ with the same vertex set su…

math.CO2015

Relating $2$ -Rainbow Domination to Roman domination

José D. Alvarado, Simone Dantas, Dieter Rautenbach

For a graph $G$ , let $γ_{R} (G)$ and $γ_{r 2} (G)$ denote the Roman domination number of $G$ and the $2$ -rainbow domination number of $G$ , respectively. It is known that $γ_{r2}(G)\leq…

math.CO2015

Dominating Sets inducing Large Components in Maximal Outerplanar Graphs

José D. Alvarado, Simone Dantas, Dieter Rautenbach

For a maximal outerplanar graph $G$ of order $n$ at least $3$ , Matheson and Tarjan showed that $G$ has domination number at most $n /3$ . Similarly, for a maximal outerplanar graph $…

math.CO2015

Strong Equality of Roman and Weak Roman Domination in Trees

Jose D. Alvarado, Simone Dantas, Dieter Rautenbach

We provide a constructive characterization of the trees for which the Roman domination number strongly equals the weak Roman domination number, that is, for which every weak Roman…

math.CO2015★ 1 cited

Relating $2$ -rainbow domination to weak Roman domination

Jose D. Alvarado, Simone Dantas, Dieter Rautenbach

Addressing a problem posed by Chellali, Haynes, and Hedetniemi (Discrete Appl. Math. 178 (2014) 27-32) we prove $γ_{r 2} (G) \leq 2 γ_{r} (G)$ for every graph $G$ , where $γ_{r 2} (G)$ and $…

math.CO2015★ 1 cited

Averaging $2$ -Rainbow Domination and Roman Domination

Jose D. Alvarado, Simone Dantas, Dieter Rautenbach

For a graph $G$ , let $γ_{r 2} (G)$ and $γ_{R} (G)$ denote the $2$ -rainbow domination number and the Roman domination number, respectively. Fujita and Furuya (Difference between 2-rainbo…

Moderate deviations of triangle counts in sparse Erdős-Rényi random graphs G(n,m) and G(n,p)

On the maximum number of minimum dominating sets in forests

Sandwiches Missing Two Ingredients of Order Four

Relating 2-Rainbow Domination to Roman domination

Dominating Sets inducing Large Components in Maximal Outerplanar Graphs

Strong Equality of Roman and Weak Roman Domination in Trees

Relating 2-rainbow domination to weak Roman domination

Averaging 2-Rainbow Domination and Roman Domination

Moderate deviations of triangle counts in sparse Erdős-Rényi random graphs $G (n, m)$ and $G (n, p)$

Relating $2$ -Rainbow Domination to Roman domination

Relating $2$ -rainbow domination to weak Roman domination

Averaging $2$ -Rainbow Domination and Roman Domination