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...

9 An acyclic coloring is a proper coloring with the additional property that the union of 10 any two color classes induces a forest. We show that every graph with maximum degree at 11 most 5 has an acyclic 7-coloring. We also show that every graph with maximum degree at 12 most r has an acyclic (1 + b (r+1) 2 4 c)-coloring. 13

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...

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...

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...

Factors influencing the phosphorus limitation of benthic microorganisms were determined for four streams (two agricultural and two forested) in central New York State over an annual cycle. Phosphorus limitation was measured biweekly as specific alkaline phosphatase activity (APA) of sediment samples. Analysis of variance showed the forested streams (sites 2 and 4) to have significantly differen...

INTRODUCTION Protecting wetland values and functions are important goals fat forest managers. Value and fimction are easy terms to confuse, but they are not interchangeable. Societal values are directly and indirectly associated with ecological functions. For example, forested wetlands may suppress f looding downstream, which is a value. Floodplain forests store water, impede flows, and dampen ...