Sheila Morais Almeida

• Professor
• Professor (Full) at Federal University of Technology of Paraná

The chromatic index, X'(G), is the smallest integer k for which a graph G has a proper edge coloring. The Classification Problem involves determining whether a graph G is Class 1 (X'(G)=Delta(G)) or Class 2 (X'(G)=Delta(G)+1), where Delta(G) is the maximum degree of G. It is known that subgraph-overfull graphs must be Class 2. In this paper we are...

An edge-coloring of a graph is an assignment of colors to the edges of a graph so that adjacent edges have distinct colors. The chromatic index of G is the smallest number of colors needed in an edge-coloring of G. Clearly, the chromatic index of G is at least its maximum degree and the celebrated Vizing’s Theorem (1964) states that, the it is at m...

Rainbow coloring problems, of noteworthy applications in Information Security, have been receiving much attention in the last years in Combinatorics. In particular, the rainbow connection number of a connected graph G, denoted rc(G), is the least k for which G admits a (not necessarily proper) k-edge-coloring such that between any pair of vertices...

The chromatic index of a graph G, χ'(G), is the least number of colors of some edge coloring of G such that no two adjacent edges have the same color. Given a graph G and an integer k, to decide if χ'(G) ≤ k is NP-complete. A graph is an interval graph if it represents the intersection relation of a set of closed intervals in R. A graph is a split...

Rainbow coloring problems, of noteworthy applications in Information Security, have been receiving much attention last years in Combinatorics. The rainbow connection number of a graph G is the least number of colors for a (not necessarily proper) edge coloring of G such that between any pair of vertices there is a path whose edge colors are all dis...

A rainbow coloring of a connected graph 𝐺 is an edge coloring that is not necessarily proper such that there is a path between any pair of vertices of 𝐺 whose edge colors are pairwise distinct. The rainbow connection number of a graph 𝐺, denoted by 𝑟𝑐(𝐺), is the least number of colors for which there is a rainbow coloring of 𝐺. A graph 𝐺 is rainbow...

Consider a vertex coloring of a graph where each color is represented by a natural number. The color sum of a vertex is the sum of the colors of its adjacent vertices. The Sigma Coloring Problem concerns determining the sigma chromatic number of a graph G, σ(G), which is the least number of colors for a coloring of G such that the color sum of any...

In a proper edge coloring of a graph, the set of colors of a vertex v is the set of colors of the edges incident to v, C(v). If C(u)≠C(v) for every adjacent vertices u and v, this edge coloring is an AVD-edge coloring. The least number of colors for which G has an AVD-edge coloring is called the AVD-chromatic index, χa′(G). We determine the AVD-chr...

We show in this paper that a split-comparability graph $G$ has chromatic index equal to $\Delta(G) + 1$ if and only if $G$ is neighborhood-overfull. That implies the validity of the Overfull Conjecture for the class of split-comparability graphs.

Given a graph G, an edge-coloring of G is an assingment of colors to the edges of G. A proper edge-coloring is an edge coloring if adjacent edges have different colors. A rainbow coloring of a connected graph G is an edge coloring that is not necessarily proper such that there is a path between any pair of vertices of G whose edge colors are pairwi...

The rainbow connection number of a connected graph G, denoted by rc(G), is the minimum number of colors needed to color the edges of G, so that every pair of vertices is connected by at least one path in which the colors of the edges are pairwise distinct. In this work we determine the rainbow connection number for the graphs Cm × Pn when m is odd...

Let F be a family of sets. The diversity of F, Υ(F), is the amount of different cardinalities on the sets of F. The class of graphs whose diversity of the maximal independent set equals Υ(F) is denoted by M(Υ(F)). Recognizing the M(t) class for a given t is a Co-NP-complete problem. However, it is possible to recognize the M(1) graphs and the simpl...

O Problema da Coloração de Arestas Distinta nos Vértices Adjacentes consiste em, dado um grafo, utilizar o menor número de cores possível para colorir suas arestas de forma que arestas incidentes no mesmo vértice tenham cores distintas e o conjunto de cores incidentes em cada vértice seja diferente dos conjuntos de cores dos seus vizinhos. Nesse tr...

The Minimum Dominating Set Problem is to find the least vertex set D such that every vertex belongs to D or is adjacent to a vertex in D. It is known that the Minimum Dominating Set Problem is NP-complete. In this work we investigate the Minimum Dominating Set Problem on lexico-graphic product of graphs. Due to a famous conjecture of V. G. Vinzing,...

Along with a result of Niessen of 1994, a conjecture proposed by Hilton and Chetwynd of 1986 implies that the chromatic index of graphs with can be determined in linear time. Connected cographs satisfy , however whether the conjecture holds for cographs is still unknown. This paper presents sufficient conditions for cographs and join graphs to be C...

The Classification Problem is the problem of deciding whether a simple graph has chromatic index equal to Δ or Δ+1. In the first case, the graphs are called Class 1, otherwise, they are Class 2. A split graph is a graph whose vertex set admits a partition into a stable set and a clique. Split graphs are a subclass of chordal graphs. Figueiredo at a...

The classification problem is the problem of deciding whether a simple graph has chromatic index equal to Δ or Δ+1. In the first case, the graphs are called Class 1, otherwise, they are Class 2. A split graph is a graph whose vertex set admits a partition into a stable set and a clique. Split graphs are a subclass of chordal graphs. C. M. H. de Fig...

The Classification Problem is the problem of deciding whether a simple graph has chromatic index equals to Δ or Δ + 1, where Δ is the maximum degree of the graph. It is known that to decide if a graph has chromatic index equals to Δ is NP-complete. A split graph is a graph whose vertex set admits a partition into a stable set and a clique. The chro...

The Classification Problem is the problem of deciding whether a simple graph has chromatic index equals to Delta or Delta + 1, where Delta is the maximum degree of the graph. It is known that to decide if a graph has chromatic index equals to Delta is NP-complete. A split graph is a graph whose vertex set admits a partition into a stable set and a...

ABSTRACT

Consider two parallel lines (denoted by r1 and r2). A graph is a PI graph (Point-Interval graph) if it is an intersection graph of a family F of triangles between r1 and r2such that each triangle has an interval with two endpoints on r1 and a vertex (a point)on r2. The family F is the PI representation of G. The PI graphs are an extension ofinterva...

We describe an ongoing project whose aim is to build a parser for Brazilian Portuguese, Selva, which can be used as a basis for subsequent research in natural language processing, such as automatic translation and ellipsis and anaphora resolution. The parser is meant to handle arbitrary prose texts in unrestricted domains, including the full range...

We describe an ongoing project whose aim is to build a parser for Brazilian Portuguese, Selva, which can be used as a basis for subsequent research in natural language processing, such as automatic translation and ellipsis and anaphora resolution. The parser is meant to handle arbitrary prose texts in unrestricted domains, including the full range...