We consider a multiagent extension of single-agent graph coloring. Multiple agents hold disjoint autonomous subgraphs of a global graph, and every color used by the agents in coloring the graph has associated cost. In this multiagent graph coloring scenario, we seek a minimum legal coloring of the global graph’s vertices, such that the coloring is also Pareto efficient, socially fair, and indiv...

Coloring graphs is one of important and frequently used topics in diverse sciences. In the majority of the articles, it is intended to find a proper bound for vertex coloring, edge coloring or total coloring in the graph. Although it is important to find a proper algorithm for graph coloring, it is hard and time-consuming too. In this paper, a new algorithm for vertex coloring, edge coloring an...

4-methylimidazole (4-mei) is a simple nitrogen-containing heterocyclic compound, and recently classified as group 2b by international agency for research on cancer (iarc). caramel coloring is widely applied food coloring in many food products including coffee, carbonated beverages, beer and wine. in present study, ɣ-irradiation was applied to caramel color iii to reduce the level of 4-mei witho...

4-Methylimidazole (4-MEI) is a simple nitrogen-containing heterocyclic compound, and recently classified as group 2B by International Agency for Research on Cancer (IARC). Caramel coloring is widely applied food coloring in many food products including coffee, carbonated beverages, beer and wine. In present study, ɣ-irradiation was applied to Caramel Color III to reduce the level of 4-MEI witho...

the robust coloring problem (rcp) is a generalization of the well-known graph coloring problem where we seek for a solution that remains valid when extra edges are added. the rcp is used in scheduling of events with possible last-minute changes and study frequency assignments of the electromagnetic spectrum. this problem has been proved as np-hard and in instances larger than 30 vertices, meta-...

‎For a coloring $c$ of a graph $G$‎, ‎the edge-difference coloring sum and edge-sum coloring sum with respect to the coloring $c$ are respectively‎ ‎$sum_c D(G)=sum |c(a)-c(b)|$ and $sum_s S(G)=sum (c(a)+c(b))$‎, ‎where the summations are taken over all edges $abin E(G)$‎. ‎The edge-difference chromatic sum‎, ‎denoted by $sum D(G)$‎, ‎and the edge-sum chromatic sum‎, ‎denoted by $sum S(G)$‎, ‎a...

{sl let $[n]={1,dots, n}$ be colored in $k$ colors. a rainbow ap$(k)$ in $[n]$ is a $k$ term arithmetic progression whose elements have different colors. conlon, jungi'{c} and radoiv{c}i'{c} cite{conlon} prove that there exists an equinumerous 4-coloring of $[4n]$ which is rainbow ap(4) free, when $n$ is even. based on their construction, we show that such a coloring of ...

let $g$ be a connected graph of order $3$ or more and $c:e(g)rightarrowmathbb{z}_k$‎ ‎($kge 2$) a $k$-edge coloring of $g$ where adjacent edges may be colored the same‎. ‎the color sum $s(v)$ of a vertex $v$ of $g$ is the sum in $mathbb{z}_k$ of the colors of the edges incident with $v.$ the $k$-edge coloring $c$ is a modular $k$-edge coloring of $g$ if $s(u)ne s(v)$ in $mathbb{z}_k$ for all pa...