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Rainbow and Monochromatic Vertex-connection of Random Graphs
A vertex-colored path P is rainbow if its internal vertices have distinct colors; whereas P is monochromatic if its internal vertices are colored the...
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A Note on the Vertex Degree Distribution of Random Intersection Graphs
We establish the asymptotic degree distribution of the typical vertex of inhomogeneous and passive random intersection graphs under minimal moment...
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Central limit theorem for the average closure coefficient
Many real-world networks exhibit the phenomenon of edge clustering,which is typically measured by the average clustering coefficient. Recently,an...
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Big Ramsey Degrees of 3-Uniform Hypergraphs Are Finite
We prove that the universal homogeneous 3-uniform hypergraph has finite big Ramsey degrees. This is the first case where big Ramsey degrees are known...
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Equitable Vertex Arboricity Conjecture Holds for Graphs with Low Degeneracy
The equitable tree-coloring can formulate a structure decomposition problem on the communication network with some security considerations. Namely,...
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An Architecture for Cooperative Mobile Health Applications
Mobile health applications are steadily gaining momentum in the modern world given the omnipresence of various mobile or Wi-Fi connections. Given...
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Lower Bounds on the Chromatic Number of Random Graphs
We prove that a formula predicted on the basis of non-rigorous physics arguments [Zdeborová and Krzakala: Phys. Rev. E (2007)] provides a lower bound...
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Range-Renewal Processes: SLLNs and Power Laws
Given n samples (viewed as an n -tuple) of a γ -regular discrete distribution π , in this article the authors concern with the weighted and unweighted...
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Rainbow k-connectivity of Random Bipartite Graphs
A path in an edge-colored graph G is called a rainbow path if no two edges of the path are colored the same color. The minimum number of colors...
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Number of edges in inhomogeneous random graphs
We study the number of edges in the inhomogeneous random graph when vertex weights have an infinite mean and show that the number of edges is O ( n log n ...
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Fractional Isomorphism of Graphons
We work out the theory of fractional isomorphism of graphons as a generalization to the classical theory of fractional isomorphism of finite graphs....
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Component Games on Random Graphs
In the (1: b ) component game played on a graph G , two players, M aker and B reaker , alternately claim 1 and b previously unclaimed edges of G ,...
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Phase Transitions and Percolation at Criticality in Enhanced Random Connection Models
We study phase transition and percolation at criticality for three random graph models on the plane, viz., the homogeneous and inhomogeneous enhanced...
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Compact graphings
Graphings are special bounded-degree graphs on probability spaces, representing limits of graph sequences that are convergent in a local...
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Covering Graphs by Monochromatic Trees and Helly-Type Results for Hypergraphs
How many monochromatic paths, cycles or general trees does one need to cover all vertices of a given r -edge-coloured graph G ? These problems were...
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Tournament Quasirandomness from Local Counting
A well-known theorem of Chung and Graham states that if h ≥ 4 then a tournament T is quasirandom if and only if T contains each h -vertex tournament...
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Moments of general time dependent branching processes with applications
We give sufficient conditions for a Crump–Mode–Jagers process to be bounded in L k for a given k > 1. This result is then applied to a recent random...