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Hardness Results for Total Rainbow Connection of Graphs

Lily Chen, Bofeng Huo, Yingbin Ma (2016)

Discussiones Mathematicae Graph Theory

A total-colored path is total rainbow if both its edges and internal vertices have distinct colors. The total rainbow connection number of a connected graph G, denoted by trc(G), is the smallest number of colors that are needed in a total-coloring of G in order to make G total rainbow connected, that is, any two vertices of G are connected by a total rainbow path. In this paper, we study the computational complexity of total rainbow connection of graphs. We show that deciding whether a given total-coloring...

Heuristic and metaheuristic methods for computing graph treewidth

François Clautiaux, Aziz Moukrim, Stéphane Nègre, Jacques Carlier (2004)

RAIRO - Operations Research - Recherche Opérationnelle

The notion of treewidth is of considerable interest in relation to NP-hard problems. Indeed, several studies have shown that the tree-decomposition method can be used to solve many basic optimization problems in polynomial time when treewidth is bounded, even if, for arbitrary graphs, computing the treewidth is NP-hard. Several papers present heuristics with computational experiments. For many graphs the discrepancy between the heuristic results and the best lower bounds is still very large. The...

Heuristic and metaheuristic methods for computing graph treewidth

François Clautiaux, Aziz Moukrim, Stéphane Nègre, Jacques Carlier (2010)

RAIRO - Operations Research

The notion of treewidth is of considerable interest in relation to NP-hard problems. Indeed, several studies have shown that the tree-decomposition method can be used to solve many basic optimization problems in polynomial time when treewidth is bounded, even if, for arbitrary graphs, computing the treewidth is NP-hard. Several papers present heuristics with computational experiments. For many graphs the discrepancy between the heuristic results and the best lower bounds is still very large....

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