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I'm reading the following paper http://www2.stat.duke.edu/~scs/Courses/Stat376/Papers/GibbsFieldEst/BesagJRSSB1974.pdf On page 7 they give the result that $$Q(\textbf{x}) = \sum_{1 \leq i \leq n} x_iG …

Suppose i have an $n \times n$ random bipartite graph and suppose that i repeat the following process $n$ times. At the start (stage 1) each edge is selected independently with probability $p(n)$, and …

I was wondering if a lot is known about independent sets in Random Geometric graphs? Most google searches don't bring up much. In addition I'm interested in any algorithms used for finding independent …

Consider the random bipartite graph with vertex classes of size $n$ and each edge being present independently with probability $p(n)$. I know one way to prove the threshold of a perfect matching is t …

Consider a random bipartite graph constructed on vertex classes of size $n$ with each edge present independently with probability $p$. How could I go about calculating the size of the expected matchin …

I've been told recently that it's better i just for help regarding my 'specific' problem rather than lots of little questions around the same topic which appear somewhat unclear. I would first like to …

I have the following problem consider a random bipartite with vertex classes $A$ and $B$ of size $|A|=|B|=\mathrm{log}^{2}(n)$ graph in which every possible edge is chosen independently with probabi …

I'm looking at a random bipartite graph $K_{\omega(n)}*K_{\omega(n)}$ where $\mathrm{log}(n)\leq \omega(n) \leq n^{1/2}$, in which each of the $\omega(n)^{2}$ edges is placed randomly with probability …

I was wondering if anyone could point me in the direction of a text or paper which would help deal with the following problem Suppose i am given a $K_{\mathrm{log}(n)} \times K_{\mathrm{log}(n)}$ bi …

Consider having a 'base' graph $G=(V,E)$ and selecting each vertex with independent probability $p$ and having the induced subgraph of $G$ with all 'selected' points as your random graph. Has this typ …