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In this paper, we show that the k-Linkage problem is polynomial-time solvable for digraphs with circumference at most 2. We also show that the directed cycles of length at least 3 have the Erdős-Pósa Property : for every n, there exists an integer tn such that for every digraph D, either D contains n disjoint directed cycles of length at least 3, or there… (More)

- Jørgen Bang-Jensen, Frédéric Havet, Ana Karolinna Maia
- Theor. Comput. Sci.
- 2015

We consider the following problem for oriented graphs and digraphs: Given a directed graphD, does it contain a subdivision of a prescribed digraph F? We give a number of examples of polynomial instances, several NP-completeness proofs as well as a number of conjectures and open problems. Key-words: NP-completeness, 2-linkage, flows, DAG and handle… (More)

- Frédéric Havet, Ana Karolinna Maia, Min-Li Yu
- Journal of the Brazilian Computer Society
- 2015

The Grundy index of a graph G =(V, E) is the greatest number of colours that the greedy edge-colouring algorithm can use on G. We prove that the problem of determining the Grundy index of a graph G=(V, E) is NP-hard for general graphs. We also show that this problem is polynomial-time solvable for caterpillars. More specifically, we prove that the Grundy… (More)

In this paper, we obtain polynomial time algorithms to determine the acyclic chromatic number, the star chromatic number, the Thue chromatic number, the harmonious chromatic number and the clique chromatic number of P4-tidy graphs and (q, q−4)-graphs, for every fixed q. These classes include cographs, P4-sparse and P4-lite graphs. All these coloring… (More)

- Victor A. Campos, Cláudia Linhares Sales, Rudini Menezes Sampaio, Ana Karolinna Maia
- Discrete Applied Mathematics
- 2014

Given a graph G= (V,E), a greedy coloring of G is a proper coloring such that, for each two colors i< j, every vertex of V (G) colored j has a neighbor with color i. The greatest k such that G has a greedy coloring with k colors is the Grundy number of G. A b-coloring of G is a proper coloring such that every color class contains a vertex which is adjacent… (More)

- Júlio Araújo, Victor A. Campos, Ana Karolinna Maia, Ignasi Sau, Ana Silva
- ArXiv
- 2017

For two positive integers k and `, a (k × `)-spindle is the union of k pairwise internally vertexdisjoint directed paths with ` arcs between two vertices u and v. We are interested in the (parameterized) complexity of several problems consisting in deciding whether a given digraph contains a subdivision of a spindle, which generalize both the Maximum Flow… (More)

- Victor A. Campos, Cláudia Linhares Sales, Ana Karolinna Maia, Nícolas A. Martins, Rudini Menezes Sampaio
- Electronic Notes in Discrete Mathematics
- 2011

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