We consider colorful bin packing games in which selfish players control a set of items which are to be packed into a minimum number of unit capacity bins. Each item has one of m ≥ 2 colors and cannot be packed next to an item of the same color. All bins have the same unitary cost which is shared among the items it contains, so that players are interested in selecting a bin of minimum shared cos...

Abstract. Coloring sparse graphs under various restrictions is a theoretical problem of significant practical relevance. Here we consider the problem of maximizing the number of different colors available at the nodes and their neighborhoods, given a predetermined number of colors. In the analytical framework of a tree approximation, solutions obtained by population dynamics show that existing ...

let g_1 and g_2 be simple connected graphs with disjoint vertex sets v(g_1) and v(g_2), respectively. for given vertices a_1in v(g_1) and a_2in v(g_2), a splice of g_1 and g_2 by vertices a_1 and a_2 is defined by identifying the vertices a_1 and a_2 in the :union: of g_1 and g_2. in this paper, we present exact formulas for computing some vertex-degree-based graph invariants of splice of graphs.

The vertex version of PI index is a molecular structure descriptor which is similar to vertex version of Szeged index. In this paper, we compute the vertex-PI index of TUC4C8(S), TUC4C8(R) and HAC5C7[r, p].

We consider the problem of fuzzy community detection in networks, which complements and expands the concept of overlapping community structure. Our approach allows each vertex of the graph to belong to multiple communities at the same time, determined by exact numerical membership degrees, even in the presence of uncertainty in the data being analyzed. We create an algorithm for determining the...

Using a Zq-generalization of a theorem of Ky Fan, we extend to Kneser hypergraphs a theorem of Simonyi and Tardos that ensures the existence of multicolored complete bipartite graphs in any proper coloring of a Kneser graph. It allows to derive a lower bound for the local chromatic number of Kneser hypergraphs (using a natural definition of what can be the local chromatic number of a uniform hy...

In this review article we summarize current knowledge on how variation on the DNA level influences human pigmentation including color variation of iris, hair, and skin. We review recent progress in the field of human pigmentation genetics by focusing on the genes and DNA polymorphisms discovered to be involved in determining human pigmentation traits, their association with diseases particularl...

The paper describes the specifics of the epidemiology of the Porcine Reproductive and Respiratory Syndrome (PRRS), that is its "behavior" as a communicable disease in porcine populations, and compares them to the general epidemiological characteristics of communicable diseases. This analysis shows that infection with the PRRS virus "behaves" epidemiologically both as an epidemic and as an endem...

Rough structures created from bulk materials at the surface could have superior durability. Superhydrophobic colorful surfaces were fabricated through chemical etching of the fiber surfaces, followed by diffusion of fluoroalkylsilane into fibers. The obtained superhydrophobic textiles show strong durability against severe abrasion, long-time laundering, and boiling water.