Chromatic spectrum of some classes of 2-regular bipartite colored graphs

Chromatic spectrum of a colored graph G is a multiset of eigenvalues of colored adjacency matrix of G. The nullity of a disconnected graph is equal to sum of nullities of its components but we show that this result does not hold for colored graphs. In this paper, we investigate the chromatic spectrum of three different classes of 2-regular bipartite colored graphs. In these classes of graphs, it is proved that the nullity of G is not sum of nullities of components of G. We also highlight some important properties and conjectures to extend this problem to general graphs.

Integumentary Colour Allocation in the Stork Family (Ciconiidae) Reveals Short-Range Visual Cues for Species Recognition

The family Ciconiidae comprises 19 extant species which are highly social when nesting and foraging. All species share similar morphotypes, with long necks, a bill, and legs, and are mostly coloured in the achromatic spectrum (white, black, black, and white, or shades of grey). Storks may have, however, brightly coloured integumentary areas in, for instance, the bill, legs, or the eyes. These chromatic patches are small in surface compared with the whole body. We have analyzed the conservatism degree of colouration in 10 body areas along an all-species stork phylogeny derived from BirdTRee using Geiger models. We obtained low conservatism in frontal areas (head and neck), contrasting with a high conservatism in the rest of the body. The frontal areas tend to concentrate the chromatic spectrum whereas the rear areas, much larger in surface, are basically achromatic. These results lead us to suggest that the divergent evolution of the colouration of frontal areas is related to species recognition through visual cue assessment in the short-range, when storks form mixed-species flocks in foraging or resting areas.

Business tourism a means of dynamising the life of local communities

The touristic expansion happens easier in a balanced climate, with standards that guarantee a constant ecologic balance and avoid the overuse of resources, pollution and any other negative impacts on the environment. MICE – Meeting, Incentive, Convention and Exhibition Industry – represents one of the industries with the highest rate of growth in the world, but unfortunately it is poorly developed in Romania. In Romania, the tourism, as a socio–economic phenomenon, integrates in the country’s economy, having the necessary conditions for accentuated growth and the optimisation of the degree of usage of the touristic stock. According to the recommendations of the World Tourism Organisation, Romania should focus on the cultural, ecologic, events and spa tourism. The prognosis of the World Tourism and Travel Council from the United States of America show that by the year 2020, the rhythm of growth of the business and events tourism in Romania will be of about 8% yearly. In this context, our country may occupy an important position in the MICE touristic activities market, if it would use the existing touristic potential and future investments in order to create favourable conditions for this type of tourism. We bring into the debate the existence of equipment which could help the business tourism, the presence of beautiful landscape areas (the Danube Delta, the Black Sea seaside, medieval cities and monasteries, touristic resorts from the Carpathians also.), presentation of the local folk traditions and crafts, the chromatic spectrum of the seasons in Romania and not lastly the folklore and gastronomy. These could be joined by the existence of a rich cultural life – especially in the large cities and touristic resorts-, the presence of museums and memorial houses, and we could not exclude the areas which have preserved their natural potential and rare fauna species. This work aims to emphasize business tourism as a sustainable form of tourism, which can lead to a relaunch in services and economic development of the local communities in a competitive international economy.

The Smallest One-Realization of a Given Set

For any set $S$ of positive integers, a mixed hypergraph ${\cal H}$ is a realization of $S$ if its feasible set is $S$, furthermore, ${\cal H}$ is a one-realization of $S$ if it is a realization of $S$ and each entry of its chromatic spectrum is either 0 or 1. Jiang et al. showed that the minimum number of vertices of a realization of $\{s,t\}$ with $2\leq s\leq t-2$ is $2t-s$. Král proved that there exists a one-realization of $S$ with at most $|S|+2\max{S}-\min{S}$ vertices. In this paper, we determine the number of vertices of the smallest one-realization of a given set. As a result, we partially solve an open problem proposed by Jiang et al. in 2002 and by Král in 2004.