By Georgiev P., Pardalos P., Theis F.

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G¨ orke, and D. 2 GHz machine. 3 Computational Results Experiments. As a reference to the benchmark, we compare our findings to an established clustering algorithm, Markov Clustering (MCL) [16], The results of the experiments with respect to performance and coverage are given in Figure 4 and 5, respectively. g. g. inter-cluster conductance, see [21]) and structural observations due to space limitations. At a first glance, the statistical results of the two absolute variants (S− cov and − Sperf ) strongly resemble each other, see Figure 4(c) and 4(d).

He proved that an optimal monotonic search strategy for a digraph needs at most one more cop than the cop number of the digraph and he conjectured that the monotonicity is held for this cops-and-robber game on digraphs. Alspach et al. [1] proposed four digraph search models in which searchers cannot be removed from digraphs. Yang and Cao [10] studied two digraph search models which are different from this paper in that all searchers and intruders must follow the edge directions when they move along edges.

A k-cycle is a cycle of length k. Similarly, a k + -cycle is a cycle of length at least k. A path component (respectively, cycle component of G is a connected component of G that is a path (respectively, cycle). Note that an isolated vertex of G is not a path component of G. For a function b mapping each vertex v of G to a nonnegative integer, a bmatching of G is a subgraph H of G such that dH (v) ≤ b(v) for all vertices v of H. When b(v) ≤ 1 for all vertices v of G, a b-matching of G is called a matching of G.

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