MOTIVATION: Gene fusion is an important evolutionary process. It can yield valuable information to infer the interactions and functions of proteins. Fused genes have been identified as non-transitive patterns of similarity in triplets of genes. To be computationally tractable, this approach usually imposes an a priori distinction between a dataset in which fused genes are searched for, and a dataset that may have provided genetic material for fusion. This reduces the 'genetic space' in which fusion can be discovered, as only a subset of triplets of genes is investigated. Moreover, this approach may have a high-false-positive rate, and it does not identify gene families descending from a common fusion event. RESULTS: We represent similarities between sequences as a network. This leads to an efficient formulation of previous methods of fused gene identification, which we implemented in the Python program FusedTriplets. Furthermore, we propose a new characterization of families of fused genes, as clique minimal separators of the sequence similarity network. This well-studied graph topology provides a robust and fast method of detection, well suited for automatic analyses of big datasets. We implemented this method in the C++ program MosaicFinder, which additionally uses local alignments to discard false-positive candidates and indicates potential fusion points. The grouping into families will help distinguish sequencing or prediction errors from real biological fusions, and it will yield additional insight into the function and history of fused genes. AVAILABILITY: FusedTriplets and MosaicFinder are published under the GPL license and are freely available with their source code at this address: http://sourceforge.net/projects/mosaicfinder. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Many graph search algorithms use a vertex labeling to compute an ordering of the vertices. We examine such algorithms which compute a peo (perfect elimination ordering) of a chordal graph and corresponding algorithms which compute an meo (minimal elimination ordering) of a non-chordal graph, an ordering used to compute a minimal triangulation of the input graph. We express all known peo-computing search algorithms as instances of a generic algorithm called MLS (maximal label search) and generalize Algorithm MLS into CompMLS, which can compute any peo. We then extend these algorithms to versions which compute an meo and likewise generalize all known meo-computing search algorithms. We show that not all minimal triangulations can be computed by such a graph search, and, more surprisingly, that all these search algorithms compute the same set of minimal triangulations, even though the computed meos are different. Finally, we present a complexity analysis of these algorithms. An extended abstract of part of this paper was published in WG 2005 .

A graph $G=(V,E)$ is a chordal probe graph if its vertices can be partitioned into two sets, P (probes) and N (non-probes), where N is a stable set and such that G can be extended to a chordal graph by adding edges between non-probes. We give several characterizations of chordal probe graphs, first, in the case of a fixed given partition of the vertices into probes and non-probes, and second, in the more general case where no partition is given. In both of these cases, our results are obtained by introducing new classes, namely, N-triangulatable graphs and cycle-bicolorable graphs. We give polynomial time recognition algorithms for each class. N-triangulatable graphs have properties similar to chordal graphs, and we characterize them using graph separators and using a vertex elimination ordering. For cycle-bicolorable graphs, which are shown to be perfect, we prove that any cycle-bicoloring of a graph renders it N-triangulatable. The corresponding recognition complexity for chordal probe graphs, given a partition of the vertices into probes and non-probes, is $O(|P||E|)$, thus also providing an interesting tractable subcase of the chordal graph sandwich problem. If no partition is given in advance, the complexity of our recognition algorithm is $O(|E|^2)$.