A5028595401- Advanced Graph Theory Research
- Graph Labeling and Dimension Problems
- Complexity and Algorithms in Graphs
- Limits and Structures in Graph Theory
- Graph theory and applications
- graph theory and CDMA systems
- Optimization and Search Problems
- Advanced Algebra and Logic
- Complex Network Analysis Techniques
- Computational Geometry and Mesh Generation
- Interconnection Networks and Systems
- Digital Image Processing Techniques
- Optimization and Packing Problems
- Advanced Topology and Set Theory
- Topological and Geometric Data Analysis
- Advanced Combinatorial Mathematics
- Scheduling and Optimization Algorithms
- Cellular Automata and Applications
- Optimization and Variational Analysis
- Stochastic processes and statistical mechanics
- Opinion Dynamics and Social Influence
- Point processes and geometric inequalities
- VLSI and FPGA Design Techniques
- Artificial Intelligence in Games
- Computability, Logic, AI Algorithms
Universidade Federal do Rio de Janeiro
2015-2024
Institute of Mathematical Sciences
2006-2019
National Council for Scientific and Technological Development
2015
Sociedade Brasileira de Educação Matemática
2015
Universidade Federal Rural do Rio de Janeiro
2007-2009
Opto Eletrônica (Brazil)
2006
Given a graph $G$ and set $S \subseteq V(G)$, we say that $S$ is $\Delta$-convex if the neighborhood of every vertex not in an independent set. A collection ${\cal V} = (V_1, V_2, \ldots , V_p)$ convex sets $p$-cover $V(G) \underset{1 \leq i p}{\bigcup} V_i$ $V_i \nsubseteq {\underset{1 j p, j\ne i}{\bigcup}} V_j$ for $i \in \{1, \ldots, p\}$. If V}$ are pairwise disjoint, $p$-partition $V(G)$. The cover number $\phi_c(G)$ (the partition $\Theta_c(G)$) least integer $p \geq 2$ which has...
Let $G$ be a finite, simple, and undirected graph let $S$ set of vertices $G$. If no vertex that does not belong to has two neighbors in $S$, then is $P_3$-convex. The $P_3$-convex hull $H_G(S)$ the smallest containing $S$. $P_3$-Carathéodory number integer $c$ such for every $u$ $H_G(S)$, there $F\subseteq S$ with $|F|\leq c$ $u\in H_G(F)$. We study structural algorithmic aspects number. characterize trees block graphs, establish upper bounds on general graphs claw-free prove it NP-complete...
A set of vertices C in a graph is convex if it contains all which lie on shortest paths between C. The hull S the smallest containing S. number $h(G)$ G cardinality whose vertex G. For connected triangle-free order n and diameter d at least 4, we prove that $h(G)\leq(n-d+3)/3$ has minimum degree 3 $h(G)\leq2(n-d+5)/7$, cubic. Furthermore for n, girth g 5, 2, d, $h(G)\leq2+(n-d-1)/\left\lceil\frac{g-1}{2}\right\rceil$. All bounds are best possible.
A walk $u_0u_1 \ldots u_{k-1}u_k$ is a \textit{weakly toll walk} if $u_0u_i \in E(G)$ implies $u_i = u_1$ and $u_ju_k\in $u_j=u_{k-1}$. set $S$ of vertices $G$ {\it weakly convex} for any two non-adjacent $x,y S$ vertex in between $x$ $y$ also $S$. The {\em convexity} the graph convexity space defined over convex sets. Many studies are devoted to determine equipped with geometry}. An \emph{extreme vertex} an element such that $S\backslash\{x\}$ convex. said be geometry it satisfies...
In 1923, Eduard Helly published his celebrated theorem, which originated the well known property. A family of subsets has property when every sub-family thereof, formed by pairwise intersecting subsets, contains a common element. Many generalizations this exist are relevant to some fields mathematics, and have several applications in computer science. work, we survey complexity aspects The main focus is on characterizations classes graphs hypergraphs related We describe algorithms for...
Graphs and Algorithms A set C of vertices a graph G is P(3)-convex if v an element for every path uvw in with u, w C. We prove that it NP-complete to decide given integer p whether the vertex can be partitioned into non-empty disjoint sets. Furthermore, we study such partitions variety classes.