We present a piecewise formula for the competition numbers of the complete tripartite graphs. For positive integers x, y and z where 2 ≤ x ≤ y ≤ z, the competition number of the complete tripartite graph Kx,y,z is yz − z − y − x + 3 whenever x 6= y and yz − 2y − z + 4 otherwise.

We compare two weakly supervised graph-based classification algorithms: spectral partitioning and tripartite updating. We provide results from empirical tests on the problem of number classification. Our results indicate (a) that both methods require minimal labeled data, (b) that both methods scale well with the number of unlabeled examples, and (c) that tripartite updating outperforms spectra...

2 Agropolis Fondation is a French foundation for scientific cooperation established in 2007 to promote and support high-level research and higher education (training-through-research) as well as to broaden international partnerships in agricultural sciences and sustainable development research. It supports a research network with scientists working on a continuum of multidisciplinary knowledge ...

399 election results as it has been thought to do.5 The Sunlight Foundation reports that less than 5% of the NRA’s campaign spending in 2012 went to races that ended with the result it was seeking. Mayor Michael Bloomberg of New York has repeatedly declared his intention to establish a well-funded electoral counterweight to the NRA to advance a “mainstream agenda” on firearm policy. President B...

Abstract A graph $H$ is common if the number of monochromatic copies in a 2-edge-colouring complete $K_n$ asymptotically minimised by random colouring. Burr and Rosta, extending famous conjecture Erdős, conjectured that every common. The conjectures Erdős Rosta were disproved Thomason Sidorenko, respectively, late 1980s. Collecting new examples graphs had not seen much progress since then, alth...