منابع مشابه
Weighting the Edge Stabilization
A modification of the edge stabilization technique is proposed to improve the behavior of the method when solving conservation equations with nonsmooth data or nonsmooth solutions. The key ingredient is tempering the edge stabilization in regions of large gradients through appropriate weights. The new method is shown to preserve the convergence properties of the original method on smooth soluti...
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A k-edge-weighting w of a graph G is an assignment of an integer weight, w(e) ∈ {1, . . . , k}, to each edge e. An edge weighting naturally induces a vertex coloring c by defining c(u) = ∑ u∼e w(e) for every u ∈ V (G). A k-edge-weighting of a graph G is vertexcoloring if the induced coloring c is proper, i.e., c(u) ≠ c(v) for any edge uv ∈ E(G). Given a graph G and a vertex coloring c0, does th...
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Modularity maximization is one of the state-of-the-art methods for community detection that has gained popularity in the last decade. Yet it suffers from the resolution limit problem by preferring under certain conditions large communities over small ones. To solve this problem, we propose to expand the meaning of the edges that are currently used to indicate propensity of nodes for sharing the...
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L. Addario-Berry et al. [Discrete Appl. Math., 2008, 156: 1168– 1174] have shown that there exists a 16-edge-weighting such that the induced vertex coloring is proper. In this note, we improve their result and prove that there exists a 13-edge-weighting of a graph G, such that its induced vertex coloring of G is proper. This result is one step close to the original conjecture posed by M. Karońs...
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2013
ISSN: 0036-1429,1095-7170
DOI: 10.1137/120867482