Confronting cliques on your unit

CheckMATE: Confronting your favourite new physics model with LHC data

In the first three years of running, the LHC has delivered a wealth of new data that is now being analysed. With over 20 fb−1 of integrated luminosity, both ATLAS and CMS have performed many searches for new physics that theorists are eager to test their model against. However, tuning the detector simulations, understanding the particular analysis details and interpreting the results can be a t...

Maximal Cliques in Unit Disk Graphs: Polynomial Approximation

We consider the problem of generating all maximal cliques in an unit disk graph. General algorithms to find all maximal cliques are exponential, so we rely on a polynomial approximation. Our algorithm makes use of certain key geographic structures of these graphs. For each edge, we limit the set of vertices that may form cliques with this as the longest edge. We then consider several characteri...

Approximation Algorithms for Maximum Cliques in 3D Unit-Disk Graphs

On Permutation Cliques

The symmetric group S , is a metric space with distance d(a , b ) = IE(a-'b)( where E ( c ) is the set of points moved by c E S,. Let L be a given subset of {I. 2, . . . , n}, a permutation clique A = A(L, n ) is any subset A c S , with d(a, b ) E L whenever a, b E A , a # b. We give a framework of new and known information o n some special A = A ( L , n): maximal, largest, largest subgroups of...

Edge-Coloring Cliques with Three Colors on All 4-Cliques

A coloring of the edges of Kn is constructed such that every copy of K4 has at least three colors on its edges. As n → ∞, the number of colors used is eO( √ log n ). This improves upon the previous probabilistic bound of O( √ n ) due to Erdős and Gyárfás.