Computing the circular chromatic number of a given planar graph is NP-complete, as it is already NP-complete to compute its chromatic number. In this note, we prove that the circular clique number of a planar graph, and therefore the circular chromatic number of a circular perfect graph, is computable in O(ne) time; outerplanar graphs are circular perfect.

We present a real-time approach for circular and polygonal road signs detection in still images, regardless of their pose and orientation. Object detection is performed using a Hough like transform based on accumulation on pairs of points with their gradients. Circular and polygonal (non triangular) traffic signs are detected by the so-called Bilateral Chinese Transform BCT. Triangular traffic ...

From observations by the Hubble Space Telescope, Keck II Telescope, and Gemini North Telescope, we have determined the mutual orbit of the large transneptunian object (174567) Varda and its satellite Ilmarë. These two objects orbit one another in a highly inclined, circular or near-circular orbit with a period of 5.75 days and a semimajor axis of 4810 km. This orbit reveals the system mass to b...

Tutte introduced the theory of nowhere zero flows and showed that a plane graph G has a face k-coloring if and only if G has a nowhere zero A-flow, for any Abelian group A with |A| ≥ k. In 1992, Jaeger et al. [9] extended nowhere zero flows to group connectivity of graphs: given an orientationD of a graph G, if for any b : V (G) → Awith  v∈V (G) b(v) = 0, there always exists a map f : E(G) →...

Using Monte Carlo simulations of a touching-bead model of double-stranded DNA, we show that DNA extension is enhanced in isosceles triangular nanochannels (relative to a circular nanochannel of the same effective size) due to entropic depletion in the channel corners. The extent of the enhanced extension depends non-monotonically on both the accessible area of the nanochannel and the apex angle...

two new species of an arbacioid echinoid, genus goniopygus, are reported for the first time from aptiansediments of baghin area, kerman, iran. the main features of the species lie in apical disc and peristomediameter. in goniopygus triangularis sp. nov., the periperoct is triangular in shape with three small, sunkentubercles, located alternatively adjacent to the periperoct, while goniopygus an...

A set of hybrid microstrip patch and semi-circular cavity antennas is introduced. The semi-circular cavity is implemented using Half-mode Substrate Integrated Waveguide (HMSIW) technique. Different shapes of patch include rectangular, semi-circular and equilateral triangular are excited using proximity effect by the circular SIW cavity at its TM010 mode of operation. The whole structures have b...

Linguists often represent the relationships between words in a collection of text as an undirected graph G = (V,E), were V is the vocabulary and vertices are adjacent in G if and only if the words they represent co-occur in a relevant pattern in the text. Ideally, the words with similar meanings give rise to the vertices of a component of the graph. However, many words have several distinct mea...