An acyclic edge coloring of a graph G is a proper edge coloring such that every cycle is colored with at least three colors. The acyclic chromatic index χa(G) of a graph G is the least number of colors in an acyclic edge coloring of G. It was conjectured that χa(G) ≤ ∆(G) + 2 for any simple graph G with maximum degree ∆(G). In this paper, we prove that every planar graph G admits an acyclic edg...

An equitable graph coloring is a proper vertex coloring, such that the size of the color classes differ by at most one. We present a flow-based scheme for generating pruning rules for enumerative algorithms such as DSATUR. The scheme models the extendability of a partial (equitable) coloring into an equitable coloring via network flows. Computational experiments show that significant reductions...

This paper presents a new algorithm for solving distributed constraint satisfaction problems (distributed CSPs) called the distributed breakout algorithm, which is inspired by the breakout algorithm for solving centraiized CSPs. In this algorithm, each agent tries to optimize its evaluation value (the number of constraint violations) by exchanging its current value and the possible amount of it...

A (proper) k-coloring of agraph G is a partition = {V1; V2; : : : ; Vk} of V (G) into k independent sets, called color classes. In a k-coloring , a vertex v∈Vi is called a Grundy vertex if v is adjacent to at least one vertex in color class Vj , for every j, j¡ i. A k-coloring is called a Grundy coloring if every vertex is a Grundy vertex. A k-coloring is called a partial Grundy coloring if eve...

In this paper, we show that for every graph of maximum average degree bounded away from d, any (d + 1)-coloring can be transformed into any other one within a polynomial number of vertex recolorings so that, at each step, the current coloring is proper. In particular, it implies that we can transform any 8-coloring of a planar graph into any other 8-coloring with a polynomial number of recolori...

Abstract The identity of the coloring agent(s) in Jupiter’s atmosphere and exact structure uppermost cloud deck are yet to be conclusively understood. Crème Brûlée model tropospheric clouds, originally proposed by Baines et al. expanded upon Sromovsky al., presumes that chromophore measured Carlson is singular agent troposphere. In this work, we test validity using spectra during Juno spacecraf...

The λ-backbone coloring is one of the various problems of vertex colorings in graphs. Given an integer λ ≥ 2, a graph G = (V,E), and a spanning subgraph (backbone) H = (V, EH) of G, a λ-backbone coloring of (G,H) is a proper vertex coloring V → {1, 2, ...} of G in which the colors assigned to adjacent vertices in H differ by at least λ. The λ-backbone coloring number BBCλ(G,H) of (G,H) is the s...

Dried carrot pomace (DCP) may be used as a thickening, coloring agent and also a carotenoid-fiber enriched component in food products formulations. The main objective of this study to investigate the effect of DCP from juice industries waste material on the physicochemical, rheological, nutritional properties of ketchup by partial replacement (0.7-3.5%) of tomato paste and the carboxy methyl ce...

We study weighted bipartite edge coloring problem, which is a generalization of two classical problems: bin packing and edge coloring. This problem has been inspired from the study of Clos networks in multirate switching environment in communication networks. In weighted bipartite edge coloring problem, we are given an edge-weighted bipartite multigraph G = (V,E) with weights w : E → [0, 1]. Th...

This paper presents a new algorithm for solving distributed constraint satisfaction problems (distributed CSPs) called the distributed breakout algorithm, which is inspired by the breakout algorithm for solving centralized CSPs. In this algorithm, each agent tries to optimize its evaluation value (the number of constraint violations) by exchanging its current value and the possible amount of it...