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Giant vacant component left by a random walk in a random d-regular graph
Random walk vacant set regular graph expanders random interlacement
2011/2/25
We study the trajectory of a simple random walk on a d-regular graph with d ≥ 3 and locally tree-like structure as the number n of vertices grows. Examples of such graphs include random d-regular grap...
There exists no distance-regular graph with intersection array {56,36,9;1,3,48}
distance-regular graph intersection array
2010/11/23
We prove that a distance-regular graph with intersection array {56,36,9;1,3,48} does not exist. This intersection array is from the table of feasible parameters for distance-regular graphs in "Distanc...
There exists no distance-regular graph with intersection array {55,36,11;1,4,45}
distance-regular graph intersection array
2010/11/12
We prove that a distance-regular graph with intersection array $\{55,36,11;1,4,45\}$ does not exist. This intersection array is from the table of feasible parameters for distance-regular graphs in "Di...
The threshold-two contact process on a random r-regular graph has a first order phase transition
The threshold-two contact process r-regular graph phase transition
2010/11/12
We consider the discrete time threshold-two contact process on a random $r$-regular graph on $n$ vertices. In this process, a vertex with at least two occupied neighbors at time $t$ will be occupied ...