8 citations · 42 across the 27 of their papers we have counts for
29 papers · 1 filter
On Grundy indices for complete geometric graphs
Dolores Lara, Christian Rubio-Montiel, Francisco Zaragoza
The pseudo-Grundy index of a graph is the largest number of colors that can be assigned to its edges, such that for every pair of colors , if then every edge colored w…
Acyclic and complete coloring of digraphs with the minimum and maximum possible numbers of colors
Mika Olsen, Christian Rubio-Montiel, Alejandra Silva Ramirez
The dichromatic and diachromatic numbers of a digraph are the minimum and maximum numbers of colors, respectively, in acyclic and complete colorings of the digraph. In this paper,…
A sharp upper bound for the harmonious total chromatic number of graphs and multigraphs
M. Abreu, J. B. Gauci, D. Mattiolo +4
A proper total colouring of a graph is called harmonious if it has the further property that when replacing each unordered pair of incident vertices and edges with their colour…
On the harmonious chromatic number of graphs
Gabriela Araujo-Pardo, Juan José Montellano-Ballesteros, Mika Olsen +1
The harmonious chromatic number of a graph is the minimum number of colors that can be assigned to the vertices of in a proper way such that any two distinct edges have dif…
Zykov sums of digraphs with diachromatic number equal to their harmonious number
Mika Olsen, Christian Rubio-Montiel, Alejandra Silva-Ramírez
The dichromatic number and the diachromatic number are generalizations of the chromatic number and the achromatic number for digraphs considering acyclic colorings. In this paper,…
Achromatic arboricity on complete graphs
Gabriela Araujo-Pardo, Christian Rubio-Montiel
In this paper we study the {\it {achromatic arboricity}} of the complete graph. This parameter arises from the arboricity of a graph as the achromatic index arises from the chromat…
The digrundy number of digraphs
Gabriela Araujo-Pardo, Juan José Montellano-Ballesteros, Mika Olsen +1
We extend the Grundy number and the ochromatic number, parameters on graph colorings, to digraph colorings, we call them {\emph{digrundy number}} and {\emph{diochromatic number}},…
Motions of a connected subgraph representing a swarm of robots inside a graph of work stations
Aarón Atilano, Sebastian Bejos, Christian Rubio-Montiel
Imagine that a swarm of robots is given, these robots must communicate with each other, and they can do so if certain conditions are met. We say that the swarm is connected if ther…
Achromatic numbers of Kneser graphs
Gabriela Araujo-Pardo, Juan Carlos Díaz-Patiño, Christian Rubio-Montiel
Complete colorings have the property that any two color classes has at least an edge between them. Parameters such as the Grundy, achromatic and pseudoachromatic numbers comes from…
Achromatic number, achromatic index and diachromatic number of circulant graphs and digraphs
Gabriela Araujo-Pardo, Juan Jos{\' e} Montellano-Ballesteros, Mika Olsen +1
In this paper, we determine the achromatic and diachromatic numbers of some circulant graphs and digraphs each one with two lengths and give bounds for other circulant graphs and d…
Extremal regular graphs of given chromatic number
Christian Rubio-Montiel
We define an extremal -graph as an -regular graph with chromatic number of minimum order. We show that the Tur{\' a}n graphs , the antihole graphs and the g…
On transversal and 2-packing numbers in uniform linear systems
Carlos A. Alfaro, G. Araujo-Pardo, C. Rubio-Montiel +1
A linear system is a pair where is a family of subsets on a ground finite set , such that , for every $l,l^\prime \in \ma…
On crossing families of complete geometric graphs
Dolores Lara, Christian Rubio-Montiel
A crossing family is a collection of pairwise crossing segments, this concept was introduced by Aronov et. al. (1994). They prove that any set of points (in general position) i…
On the 4-girth-thickness of the line graph of the complete graph
Christian Rubio-Montiel
The -girth-thickness of a graph is the minimum number of planar subgraphs of girth at least whose union is . In this note, we give the -girth-thickness $θ…
The diachromatic number of digraphs
Gabriela Araujo-Pardo, Juan José Montellano-Ballesteros, Mika Olsen +1
We consider the extension to directed graphs of the concept of achromatic number in terms of acyclic vertex colorings. The achromatic number have been intensely studied since it wa…
On chromatic indices of finite affine spaces
Gabriela Araujo-Pardo, György Kiss, Christian Rubio-Montiel +1
The pseudoachromatic index of the finite affine space denoted by is the the maximum number of colors in any complete line-coloring of $\…
The 4-girth-thickness of the complete multipartite graph
Christian Rubio-Montiel
The -girth-thickness of a graph is the smallest number of planar subgraphs of girth at least whose union is . In this paper, we calculate the -girth-thick…
Complete colorings of planar graphs
M. Gabriela Araujo-Pardo, F. Esteban Contreras-Mendoza, Sara J. Murillo-García +2
In this paper, we study the achromatic and the pseudoachromatic numbers of planar and outerplanar graphs as well as planar graphs of girth 4 and graphs embedded on a surface. We gi…
The 4-girth-thickness of the complete graph
Christian Rubio-Montiel
In this paper, we define the -girth-thickness of a graph as the minimum number of planar subgraphs of girth at least whose union is . We obtain the -girth…
On line colorings of finite projective spaces
Gabriela Araujo-Pardo, György Kiss, Christian Rubio-Montiel +1
In this paper, we prove lower and upper bounds on the achromatic and the pseudoachromatic indices of the -dimensional finite projective space of order .
The Hadwiger number, chordal graphs and -perfection
Christian Rubio-Montiel
A graph is chordal if every induced cycle has three vertices. The Hadwiger number is the order of the largest complete minor of a graph. We characterize the chordal graphs in terms…
Coloring decompositions of complete geometric graphs
Clemens Huemer, Dolores Lara, Christian Rubio-Montiel
A decomposition of a non-empty simple graph is a pair , such that is a set of non-empty induced subgraphs of , and every edge of belongs to exactly one subgra…
On two-quotient strong starters for
Carlos A. Alfaro, Christian Rubio-Montiel, Adrián Vázquez-Ávila
Let be a finite additive abelian group of odd order , and let be the set of non-zero elements. A starter for is a set $S=\{\{x_i,y_i\}:i=1,\ldots,\…
Pseudoachromatic and connected-pseudoachromatic indices of the complete graph
G. Araujo-Pardo, C. Rubio-Montiel
A complete -coloring of a graph is a (not necessarily proper) -coloring of the vertices of , such that each pair of different colors appears in an edge. A complete …