The concept of circular chromatic number of graphs was introduced by Vince(1988). In this paper we define circular chromatic number of uniform hypergraphs and study their basic properties. We study the relationship between circular chromatic number with chromatic number and fractional chromatic number of uniform hypergraphs.

An intelligent learning-based approach using neural network and fuzzy logic to the problem of interference canceling is proposed in the paper. The famous signal-processing structure of adaptive noise canceling is used for the research of interference signal canceling, in which a neuro-fuzzy system is used as the adaptive notch filter. Four T-S fuzzy rules are in the neuro-fuzzy filter. The filt...

The chromatic polynomial gives the number of proper λ-colourings of a graph G. This paper considers factorisation of the chromatic polynomial as a first step in an algebraic study of the roots of this polynomial. The chromatic polynomial of a graph is said to have a chromatic factorisation if P (G,λ) = P (H1, λ)P (H2, λ)/P (Kr , λ) for some graphs H1 and H2 and clique Kr. It is known that the c...

In this note we consider s-chromatic polynomials for finite simplicial complexes. When s = 1, the 1-chromatic polynomial is just the usual graph chromatic polynomial of the 1-skeleton. In general, the s-chromatic polynomial depends on the s-skeleton and its value at r is the number of (r, s)-colorings of the simplicial complex.

For a graph G, let P(G; ) be its chromatic polynomial and let [G] be the set of graphs having P(G; ) as their chromatic polynomial. We call [G] the chromatic equivalence class of G. If [G]={G}, then G is said to be chromatically unique. In this paper, we 4rst determine [G] for each graph G whose complement 5 G is of the form aK1∪bK3∪⋃16i6s Pli , where a; b are any nonnegative integers and li is...

For the purpose of meeting the requirement for image chromatic information storage, data processing and transmission in turbulence precise detection, this paper presents a new data optimization method of turbulence image chromatic data based on energy optimization surface construction and multi-order Random Sample Consensus (RANSAC) estimation. Though extracting turbulence image’s chromatic dat...

We prove the conjecture of A. Postnikov that (A) the number of regions in the inversion hyperplane arrangement associated with a permutation w ∈ Sn is at most the number of elements below w in the Bruhat order, and (B) that equality holds if and only if w avoids the patterns 4231, 35142, 42513 and 351624. Furthermore, assertion (A) is extended to all finite reflection groups. A byproduct of thi...

In this short note we observe that recent results of Abért and Hubai and of Csikvári and Frenkel about Benjamini–Schramm continuity of the holomorphic moments of the roots of the chromatic polynomial extend to the theory of dense graph sequences. We offer a number of problems and conjectures motivated by this observation.

Abstract In this paper we obtain the explicit formulas for chromatic polynomials of cacti. From the results relating to cacti we deduce the analogous formulas for the chromatic polynomials of n–gon–trees. Besides, we characterize unicyclic graphs by their chromatic polynomials. We also show that the so–called clique–forest–like graphs are chromatically equivalent.

Discrimination for equiluminant chromatic stimuli that vary in L- and M-cone excitation depends on the chromaticity difference between the test field and the surrounding area. The current study investigated the effect of the proximity in space and time of a surround to the test field on chromatic contrast discrimination. The experimental paradigm isolated spatial, temporal, and spatial-and-temp...