An r-circular coloring of a graph G is a map f from V(G) to the set of open unit intervals of an Euclidean circle of length r, such that f(u) ∩ f(v) = Ф whenever uv ∈ E(G). Circular perfect graphs are defined analogously to perfect graphs by means of two parameters, the circular chromatic number and the circular clique number. In this paper, we study the properties of circular perfect graphs. We give (1) a necessary condition for a graph to be circular perfect, (2) some circular critical imperfect graphs, and (3) a characterization of graphs with the property that each of their induced subgraphs has circular clique number the same as its clique number, and then the two conjectures that are equivalent to the perfect graph conjecture.
The circular clique number of a graph G is the maximum fractional k/d such that G^kd admits a homomorphism to G. In this paper, we give some sufficient conditions for graphs whose circular clique number equal the clique number, we also characterize the K1,3-free graphs and planar graphs with the desired property.
The traditional correlation-based detector is optimal only for Gaussian data, but the Laplacian Probability Density Function (PDF) is more appropriate to model the coefficients in the Discrete Ridgelet Transform (DRT) domain. An additive maximum-likelihood detector based on the Laplacian PDF is analyzed and the theoretical result of its performance is given. The experiments show that the error of the Laplacian model for the DRT coefficients of many images is smaller than that of the Gaussian model. The experiments also prove that the Laplacian detector is superior to the tradi- tional correlation-based detector.
