Let ∆(G) be the maximum degree of a graph G. Brooks’ theorem states that the only connected graphs with chromatic number χ(G) = ∆(G) + 1 are complete graphs and odd cycles. We prove a fractional analogue of Brooks’ theorem in this paper. Namely, we classify all connected graphs G such that the fractional chromatic number χf (G) is at least ∆(G). These graphs are complete graphs, odd cycles, C 2...

The Brooks’ Law says that adding manpower to a late software project makes it later. Brooks developed the law through observation of many projects and derived the generalization. His explanation was quite reasonable and convincing. However, it becomes a debilitating statement to any software project manager who is faced with a late project. This paper presents an in-depth study of Brooks’ Law u...

predictions of suspended sediment load for soolegan river, iran using selected empirical equ-ations were made based on 355 data sets. data include flow discharges from 3.11 m3/s to 43.81 m3/s, flow velocities from 0.22 m/s to 1.03 m/s, and flow depths from 0.5 to 1.03 m. equations of einstein (1950), bagnold (1966), toufalleti (1968), brooks (1963), chang-simons-richardson(1965),lane-kalinske (...