Cláudia Linhares Sales

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Two non-adjacent vertices x and y in a graph G form an even pair if every induced path between them has an even number of edges. For a given pair fx; yg in a graph G, we denote by G xy the graph obtained from G by contracting x and y. In 1982, Fonlupt and Uhry proved that if G is perfect then so is G xy. In 1987, Meyniel used this fact to prove that no(More)
An even pair in a graph is a pair of non-adjacent vertices such that every chord-less path between them has even length. A graph is called strict quasi-parity when every induced subgraph that is not a clique has an even pair, and it is called perfectly contractile when every induced subgraph can be turned into a clique through a sequence of even-pair(More)
A b-coloring is a coloring of the vertices of a graph such that each color class contains a vertex that has a neighbor in all other color classes. The b-chromatic number of a graph G is the largest integer k such that G admits a b-coloring with k colors. A graph is b-perfect if the b-chromatic number is equal to the chromatic number for every induced(More)
A coloring c of a graph G = (V, E) is a b-coloring if in every color class there is a vertex colored i whose neighborhood intersects every other color classes. The b-chromatic number of G, denoted χ b (G), is the greatest integer k such that G admits a b-coloring with k colors. A graph G is tight if it has exactly m(G) vertices of degree m(G) − 1, where(More)
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt età la diffusion(More)
—Given an undirected graph G = (V, E) and a weight function w : V → R + , a vertex coloring of G is a partition of V into independent sets, or color classes. The weight of a vertex coloring of G is defined as the sum of the weights of its color classes, where the weight of a color class is the weight of a heaviest vertex belonging to it. In the W(More)
The Grundy number of a graph G is the largest number of colors used by any execution of the greedy algorithm to color G. The problem of determining the Grundy number of G is polynomial if G is a P 4-free graph and N P-hard if G is a P 5-free graph. In this article, we define a new class of graphs, the fat-extended P 4-laden graphs, and we show a polynomial(More)