Eating takes place in a context of environmental stimuli known as ambience. Various external factors such as social and physical surroundings, including the presence of other people and sound, temperature, smell, color, time, and distraction affect food intake and food choice. Food variables such as the temperature, smell, and color of the food also influence food intake and choice differently....

Multi-coloring problem is a generalization of the well known Graph coloring problem which is known to be NP-hard. Multi-coloring problem can be solved by algorithms designed for the graph coloring problem after transformation of the graphs. However, since the graph transformations increase the size and order of the given graph, in some cases, it may be impractical to solve multi-coloring proble...

Vertex coloring of a graph is the assignment of labels to the vertices of the graph so that adjacent vertices have different labels. In the case of polyhedral graphs, the chromatic number is 2, 3, or 4. Edge coloring problem and face coloring problem can be converted to vertex coloring problem for appropriate polyhedral graphs. We have been developed an interactive learning system of polyhedra,...

Let $G=(V(G),E(G))$ be a simple, finite and undirected graph of order $n$. A $k$-vertex weightings of a graph $G$ is a mapping $w: V(G) to {1, ldots, k}$. A $k$-vertex weighting induces an edge labeling $f_w: E(G) to N$ such that $f_w(uv)=w(u)+w(v)$. Such a labeling is called an {it edge-coloring k-vertex weightings} if $f_{w}(e)not= f_{w}(echr(chr(chr('39')39chr('39'))39chr(chr('39')39chr('39'...

If a graph G contains no subgraph isomorphic to some graph H, then G is called H-free. A coloring of a graph G = (V,E) is a mapping c : V → {1, 2, . . .} such that no two adjacent vertices have the same color, i.e., c(u) 6= c(v) if uv ∈ E; if |c(V )| ≤ k then c is a k-coloring. The Coloring problem is to test whether a graph has a coloring with at most k colors for some integer k. The Precolori...

An L(2, 1)-coloring of a graph G is a coloring of G’s vertices with integers in {0, 1, . . . , k} so that adjacent vertices’ colors differ by at least two and colors of distance-two vertices differ. We refer to an L(2, 1)-coloring as a coloring. The span λ(G) of G is the smallest k for which G has a coloring, a span coloring is a coloring whose greatest color is λ(G), and the hole index ρ(G) of...

Many classes of graphs where the vertex coloring problem is polynomially solvable are known, the most prominent being the class of perfect graphs. However, the list-coloring problem is NP-complete for many subclasses of perfect graphs. In this work we explore the complexity boundary between vertex coloring and list-coloring on such subclasses of perfect graphs, where the former admits polynomia...