Graph coloring and its generalizations are useful tools in modeling a wide variety of scheduling and assignment problems. In this paper we review several variants of graph coloring, such as precoloring extension, list coloring, multicoloring, minimum sum coloring, and discuss their applications in scheduling.

We consider two problems, namely Min Split-coloring and Min Cocoloring, that generalize the classical Min Coloring problem by using not only stable sets but also cliques to cover all the vertices of a given graph. We prove the NP-hardness of some cases. We derive approximation results for Min Split-coloring and Min Cocoloring in line graphs, comparability graphs and general graphs. This provide...

A proper coloring of a graph is odd if every non-isolated vertex has some color that appears an number times on its neighborhood. This notion was recently introduced by Petruševski and Škrekovski, who proved planar admits 9-coloring; they also conjectured 5-coloring. Shortly after, this conjecture confirmed for graphs girth at least seven Cranston; outerplanar Caro, Petruševski, Škrekovski. Bui...

Graph coloring has numerous applications and is a wellknown NP-complete problem. The goal of this paper is to survey recent results of the authors on coloring and improper coloring of sparse graphs and to point out some polynomial-time algorithms for coloring (not necessarily optimal) of graphs with bounded maximum average degree. Mathematics Subject Classification: 05C15, 05C35

An adjacent vertex distinguishing edge-coloring or an avd-coloring of a simple graph G is a proper edge-coloring of G such that no pair of adjacent vertices meets the same set of colors. We prove that every graph with maximum degree ∆ and with no isolated edges has an avd-coloring with at most ∆ + 300 colors, provided that ∆ > 1020. AMS Subject Classification: 05C15

We prove that the intersection hypergraph of a family of n pseudo-disks with respect to another family of pseudo-disks admits a proper coloring with 4 colors and a conflict-free coloring with O(log n) colors. Along the way we prove that the respective Delaunay-graph is planar. We also prove that the intersection hypergraph of a family of n regions with linear union complexity with respect to a ...

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....

A majority coloring of a directed graph is vertex-coloring in which every vertex has the same color as at most half its out-neighbors. Kreutzer, Oum, Seymour, van der Zypen and Wood proved that digraph $4$-coloring conjectured admits $3$-coloring. They observed Local Lemma implies conjecture for digraphs large enough minimum out-degree if, crucially, maximum in-degree bounded by a(n exponential...

Spices play a vital role in Indian cuisine since long time. These are the some of most valuable items domestic as well industrial kitchens. The spices is to increase palatability and used flavoring, coloring, preservative agents. Rather than cooking part many industry like medical, cosmetic, pharmaceutical perfumery, more. In current, study explores kitchen medical it acts anti-proliferative, a...

This study determines the possibility of using spread (SC) and compound chocolate (CC) as delivering agents betalains, bioactive compounds coloring agents. Therefore, effects various beetroot powder concentrations (0.0-1.00 g/100 g) on SC CC’s quality parameters associated visual properties over a 12-week period under accelerated shelf-life conditions were investigated. The hardness plastic vis...