Dvo?ák and Postle introduced the concept of DP-coloring to overcome some difficulties in list coloring. Sittitrai Nakprasit combined defective coloring define a new coloring—relaxed DP-coloring. For relaxed DP-coloring, Sribunhung et al. proved that planar graphs without 4- 7-cycles are DP-(0, 2, 2)-colorable. Li 4, 8-cycles or 9-cycles DP-(1, 1, 1)-colorable. Lu Zhu 5-cycles, 6-cycles, In this...

Motivated by a frequency assignment problem in cellular networks, we introduce and study a new coloring problem that we call Minimum Conflict-Free Coloring (Min-CF-Coloring). In its general form, the input of the Min-CF-coloring problem is a set system (X;S), where each S 2 S is a subset of X . The output is a coloring of the sets in S that satisfies the following constraint: for every x 2 X th...

In this paper, we consider distributed coloring for planar graphs with a small number of colors. We present an optimal (up to a constant factor) O(logn) time algorithm for 6-coloring planar graphs. Our algorithm is based on a novel technique that in a nutshell detects small structures that can be easily colored given a proper coloring of the rest of the vertices and removes them from the graph ...

Graph coloring is used in wireless networks to optimize network resources: bandwidth and energy. Nodes access the medium according to their color. It is the responsibility of the coloring algorithm to ensure that interfering nodes do not have the same color. In this research report, we focus on wireless sensor networks with grid topologies. How does a coloring algorithm take advantage of the re...

A coloring of edges of a finite directed graph turns the graph into finite-state automaton. The synchronizing word of a deterministic automaton is a word in the alphabet of colors (considered as letters) of its edges that maps the automaton to a single state. A coloring of edges of a directed graph of uniform outdegree (constant outdegree of any vertex) is synchronizing if the coloring turns th...

In this paper, we describe a coloring method of gray-level images in a restricted area based on neural networks. The coloring method employs color clustering and classiication algorithms to images in an application area. In this research, the self-organizing feature map algorithm for clustering is applied to construction of a codebook. Variations of intensity in the gray-level image are classii...