Specifications for problem set A of random graphs
Note! The problem set consists of two parts: Part I: The problem specifications pages Part II: The answer pages
... The problem set consists of two parts: • Part I, the problem specifications pages (numbered pages 1 to 8), define the rules to follow and the questions to be ...
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Note! The problem set consists of two parts: Part I: The problem specifications pages Part II: The answer pages
... • Written text. A sub - problem shall be answered by written text. In that case the answer shall be written in the supplied marked box in the answer page. The answer can give from 0 to max X points . • True or ...
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Treewidth of Erdős–Rényi random graphs, random intersection graphs, and scale-free random graphs
... The notion of d-rigid and balanced partition generalizes that of balanced partition by requiring that any vertex set of size at most d in the larger subset of a partition cannot be moved to the other subset of the ...
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A PTAS for the minimum dominating set problem in unit disk graphs
... disk graphs are widely used to model the communication in wireless ad-hoc networks ...storm problem. A message broadcast only in the dominating set is an efficient way to ensure that it is received by ...
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Random rectangular graphs
... the random geometric graph (RGG) model is proposed by considering a set of points uniformly and independently distributed on a rectangle of unit area instead of on a unit square [0, 1] 2 ...the ...
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Random walks on graphs
... p We can now compute the cover time of S. Let A be the set of leaves of this tree. Let vertex i be the vertex whose distance to the closest leaf is i = 0, 1, . . . , r. So i = 0 if we start from a leaf and i = r ...
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Continuum limit of the nonlocal p-Laplacian evolution problem on random inhomogeneous graphs
... The random graph models defined above are ”homogeneous” in the sense that all vertices are exactly equivalent in the definition of the ...real-world graphs are ...new random graph models designed to ...
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Sampling random colorings of sparse random graphs
... important problem in many ...on random colorings, which are an example of a spin sys- tem, corresponding to the zero-temperature limit of the anti-ferromagnetic Potts ...
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Synchronizability of random rectangular graphs
... one problem of fundamental interest for the analysis of synchronization in a RGG is the influence of the geometric shape of the region, where the nodes are located, on the synchronizability of the resulting ...
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On the diameter of random planar graphs
... a random connected labelled planar graph with n vertices and ⌊µn⌋ edges is in the interval (n 1/4−ǫ , n 1/4+ǫ ) ...of random planar ...well-studied problem of the radius of random ...a ...
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Group walk random graphs
... between random walks and electrical networks as introduce by Doyle & Snell ...Dirichlet problem has the unique trivial solution v(x) = 1 for every x ∈ V (G n ...Dirichlet problem can be obtained as ...
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Epidemics on random intersection graphs
... at random, is ultimately infected by a major outbreak is ρ b ...at random, j 1 and j 2 say, and construct their susceptibility sets on a generation basis as above, stopping each process after t n ...
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Synchronizability of random rectangular graphs
... one problem of fundamental interest for the analysis of synchronization in a RGG is the influence of the geometric shape of the region, where the nodes are located, on the synchronizability of the resulting ...
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Threshold phenomena in random graphs
... 1950s, random graphs appeared for the first time in a result of the prolific hungarian mathematician Pál ...in random graph theory has only grown up until ...were set, while they were mainly ...
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Geometric Inhomogeneous Random Graphs
... hyperbolic random graph model, we first sample the radii, then the angles and at last the ...a set of radii (r 1 , ...the random positions x u and the edge probabilities p uv (x u , x v ) produced by ...
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Universality of Cutoff for Random Walks on Random Cayley Graphs
... non-Abelian groups, this simple projection does not hold; just looking at W (t) loses information. Recall that the invariant distribution is uniform, regardless of the group. For an Abelian group G, we propose as the ...
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Packing tree factors in random and pseudo-random graphs
... • d(v) > (1 − )np for every vertex v. • d(u, v) 6 (1 + )np 2 for every pair of distinct vertices u and v. Here, d(v) denotes the degree of vertex v, and d(u, v) denotes the co-degree of u and v, i.e., the number of ...
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On a labeling problem in graphs
... It follows from Lemma 4 that covering the three edges of K 3 by assigning the same label, say ‘‘a’’, at nodes v , w , and x, does not affect the outcome of the covering problem. Thus, without loss of generality, ...
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Parameterized complexity of the weighted independent set problem beyond graphs of bounded clique number
... problem becomes fixed-parameter ...for graphs without large cliques, which follows from a simple Ramsey argument (see ...the problem for graphs of bounded degree, of bounded degeneracy, of ...
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Lazy Cops and Robbers played on random graphs and graphs on surfaces
... 1.1. Definitions and notation. We consider only finite, undirected graphs in this paper. For background on graph theory, the reader is directed to [27]. The game of Cops and Robbers was independently introduced in ...
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