A5035111977- Advanced Graph Theory Research
- Graph Labeling and Dimension Problems
- Limits and Structures in Graph Theory
- graph theory and CDMA systems
- Graph theory and applications
- Computational Geometry and Mesh Generation
- Finite Group Theory Research
- Optimization and Search Problems
- Nuclear Receptors and Signaling
- Modular Robots and Swarm Intelligence
- Advanced Topology and Set Theory
- Coding theory and cryptography
- Advanced Combinatorial Mathematics
- Mathematics and Applications
- Topological and Geometric Data Analysis
- Robotic Path Planning Algorithms
- Nanocluster Synthesis and Applications
- Advanced Algebra and Logic
- Optimization and Packing Problems
- Metaheuristic Optimization Algorithms Research
- Cryptography and Residue Arithmetic
- Scheduling and Timetabling Solutions
Universidad Nacional Autónoma de México
2014-2024
Comenius University Bratislava
2016-2019
Center for Research and Advanced Studies of the National Polytechnic Institute
2017-2019
Eötvös Loránd University
2017
Instituto Politécnico Nacional
2017
A proper total colouring of a graph $G$ is called harmonious if it has the further property that when replacing each unordered pair incident vertices and edges with their colours, then no colours appears twice. The smallest number for to exist chromatic $G$, denoted by $h_t(G)$. Here, we give general upper bound $h_t(G)$ in terms order $n$ $G$. Our two main results are obvious consequences computation complete $K_n$ multigraph $\lambda K_n$, where $\lambda$ joining $K_n$. In particular,...
A proper total colouring of a graph G is called harmonious if it has the further property that when replacing each unordered pair incident vertices and edgeswith their colours, then no colours appears twice. The smallest number for to exist chromatic G, denoted by ht(G). Here, we give general upper bound ht(G) in terms order n G. Our two main results are obvious consequences computation complete Kn multigraph λKn, where λ edges joining Kn. In particular, Araujo-Pardo et al. have recently...
We consider the extension to directed graphs of concept achromatic number in terms acyclic vertex colorings. The have been intensely studied since it was introduced by Harary, Hedetniemi and Prins 1967. dichromaticnumber is a generalization chromatic for digraphs defined Neumann-Lara 1982. A coloring digraph an if each subdigraph induced class acyclic, complete any pair classes $x,y$, there arc from $x$ $y$ $x$. dichromatic diachromatic numbers are, respectively, smallest largest colors...
A graph $G$ is \emph { trivially perfect } if for every induced subgraph the cardinality of largest set pairwise nonadjacent vertices ( stability number ) $\alpha(G)$ equals maximal cliques $m(G)$ . We characterize graphs in terms vertex- coloring and we extend some definitions to infinite
Some new infinite families of simple, indecomposable m-factorizations the complete multigraph λKv are presented. Most constructions come from finite geometries.
A linear system is a pair (P,L) where L family of subsets on ground finite set P, such that |l∩l′|≤1, for every l,l′∈L. The elements P and are called points lines, respectively, the intersecting if any lines intersect in exactly one point. subset T transversal intersects line, number, τ(P,L), minimum order transversal. On other hand, 2-packing R three them have common point, then number (P,L), ν2(P,L), size maximum set. It known τ(P,L) bounded above by quadratic function ν2(P,L). An open...
In this paper, we define the 4-girth-thickness θ(4, G) of a graph G as minimum number planar subgraphs girth at least 4 whose union is G. We prove that an arbitrary complete Kn, Kn), ⌈(n+2)/4⌉ for n ≠ 6, 10 and K6)=3.
The g -girth-thickness θ ( , G ) of a graph is the smallest number planar subgraphs girth at least whose union . In this paper, we calculate 4 (4, complete m -partite when each part has an even vertices.
In this paper, we explore the application of a particular genetic algorithm, Rank Genetic Algorithm (Rank GA), to address graph theory problem. The GA was introduced problem coloring, exploring into specialized field Chromatic Graph Theory. We successfully improved several previously known lower bounds. To validate effectiveness these new bounds, performed an analytical approximation, confirming their validity. findings underscore interdisciplinary impact use algorithms in theoretical...
We study an extension to directed graphs of the parameter called $b$-chromatic number a graph in terms acyclic vertex colorings: dib-chromatic number. give general bounds for this parameter. also show some results about tournaments and regular digraphs.
We present some results on the harmonious colourings of Levi graph a 2-design, focusing Steiner 2-design. It is easily seen that chromatic number such at least points design: we study and construct Banff designs, designs this lower bound attained.
In this paper, we give a relationship between the covering number of simple graph \(G\), \(\beta(G)\), and new parameter associated to which is called 2-degree-packing \(\nu_2(G)\). We prove that \[\lceil \nu_{2}(G)/2\rceil\leq\beta(G)\leq\nu_2(G)-1,\] for any with \(|E(G)|>\nu_2(G)\). Also, characterization connected graphs attain equalities.