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- Paul Dorbec, Ingo Schiermeyer, Elzbieta Sidorowicz, Ã‰ric Sopena
- Discrete Applied Mathematics
- 2014

An edge-coloured graph G is said to be rainbow-connected if any two vertices are connected by a path whose edges have different colours. The rainbow connection number of a graph is the minimum numberâ€¦ (More)

- Paul Dorbec, Michael A. Henning, Douglas F. Rall
- J. Comb. Optim.
- 2008

In this paper we continue the investigation of total domination in Cartesian products of graphs first studied in Graphs Combin. 21 (2005), 63â€“69. A set S of vertices in a graph G is a totalâ€¦ (More)

- Paul Dorbec, Michel Mollard
- Electr. J. Comb.
- 2005

We introduce and study a common generalization of 1-error binary perfect codes and perfect single error correcting codes in Lee metric, namely perfect codes on products of paths of length 2 and ofâ€¦ (More)

- Bostjan Bresar, Paul Dorbec, +4 authors Douglas F. Rall
- Journal of Graph Theory
- 2012

Vizingâ€™s conjecture from 1968 asserts that the domination number of the Cartesian product of two graphs is at least as large as the product of their domination numbers. In this paper we survey theâ€¦ (More)

- Paul Dorbec, Sylvain Gravier, GÃ¡bor N. SÃ¡rkÃ¶zy
- Journal of Graph Theory
- 2008

In any r-uniform hypergraph H for 2 â‰¤ t â‰¤ r we define an r-uniform t-tight Berge-cycle of length l, denoted by C (r,t) l , as a sequence of distinct vertices v1, v2, . . . , vl, such that for eachâ€¦ (More)

- Paul Dorbec, MickaÃ«l Montassier, Pascal Ochem
- Journal of Graph Theory
- 2014

A cograph is a graph that contains no path on four vertices as an induced subgraph. A cograph k-partition of a graph G = (V,E) is a vertex-partition of G into k sets V1, . . . , Vk âŠ‚ V so that theâ€¦ (More)

- Paul Dorbec, Michel Mollard, Sandi Klavzar, Simon Spacapan
- SIAM J. Discrete Math.
- 2008

The power system monitoring problem asks for as few as possible measurement devices to be put in an electric power system. The problem has a graph theory model involving power dominating sets inâ€¦ (More)

- Gerard J. Chang, Paul Dorbec, MickaÃ«l Montassier, AndrÃ© Raspaud
- Discrete Applied Mathematics
- 2012

In this paper, we introduce the concept of k-power domination which is a common generalization of domination and power domination. We extend several known results for power domination to k-powerâ€¦ (More)

- Paul Dorbec, Michael A. Henning, Christian LÃ¶wenstein, MickaÃ«l Montassier, AndrÃ© Raspaud
- SIAM J. Discrete Math.
- 2013

In this paper, we continue the study of power domination in graphs (see SIAM J. Discrete Math. 15 (2002), 519â€“529; SIAM J. Discrete Math. 22 (2008), 554â€“567; SIAM J. Discrete Math. 23 (2009),â€¦ (More)

- Paul Dorbec, Sandi Klavzar
- 2014

The recently introduced concept of k-power domination generalizes domination and power domination, the latter concept being used for monitoring an electric power system. The k-power dominationâ€¦ (More)