We present a comprehensive approach to the modeling, performance analysis, and design of clustered molecular nanonetworks in which nano-machines different clusters release an appropriate number molecules transmit their sensed information respective fusion centers. The centers decode this by counting received given time slot. Owing propagation properties biological media, setup suffers from both...

Haj\'os conjectured that every graph containing no subdivision of the complete $K_{s+1}$ is properly $s$-colorable. This conjecture was disproved by Catlin. Indeed, maximum chromatic number such graphs $\Omega(s^2/\log s)$. We prove $O(s)$ colors are enough for a weakening this only requires monochromatic component to have bounded size (so-called clustered coloring). Our approach leads more res...