A Fully Dynamic Distributed Algorithm for a B-Coloring of Graphs

A b-coloring of a graph G is a proper coloring of the nodes of G such that each color class contains a node that has a neighbor in all other color classes. A fully dynamic algorithm is an algorithm used to support modifications (insertion or deletion) of nodes and edges in a network. Thus, in this paper we propose a fully dynamic distributed algorithm to maintain a b-coloring of a graph when its topology evolves. This method determines a b-coloring in time O(¿2) and needs O(n¿) changes of colors to maintain a b-coloring of a graph, where n is the number of nodes and ¿ is the maximum degree in the graph.

[1]  Chính T. Hoàng,et al.  On the b-dominating coloring of graphs , 2005, Discret. Appl. Math..

[2]  Taoufik Faik,et al.  About the b-continuity of graphs: (Extended Abstract) , 2004, Electron. Notes Discret. Math..

[3]  Zsolt Tuza,et al.  On the b-Chromatic Number of Graphs , 2002, WG.

[4]  Saurabh Srivastava,et al.  Distributed algorithms for finding and maintaining a k-tree core in a dynamic network , 2003, Inf. Process. Lett..

[5]  Christian Lavault,et al.  A distributed algorithm for constructing a minimum diameter spanning tree , 2004, J. Parallel Distributed Comput..

[6]  Janez Zerovnik,et al.  2-local Distributed Algorithms for Generalized Coloring of Hexagonal Graphs , 2005, Electron. Notes Discret. Math..

[7]  Hamamache Kheddouci,et al.  Exact values for the b-chromatic number of a power complete k-ary tree , 2005 .

[8]  Taoufik Faik.  About the b-Continuity of Graphs , 2004, CTW.

[9]  Mario Valencia-Pabon,et al.  On Approximating the B-Chromatic Number , 2003, Discret. Appl. Math..

[10]  Hamamache Kheddouci,et al.  The b-chromatic number of power graphs , 2003, Discret. Math. Theor. Comput. Sci..

[11]  Hamamache Kheddouci,et al.  Discussion on the (partial) Grundy and b-chromatic numbers of graphs , 2008 .

[12]  Shing-Tsaan Huang,et al.  A Self-Stabilizing Algorithm for Maximal Matching , 1992, Inf. Process. Lett..

[13]  Wayne Goddard,et al.  An anonymous self-stabilizing algorithm for 1-maximal independent set in trees , 2004, Inf. Process. Lett..

[14]  Manouchehr Zaker,et al.  Bounds for the b-chromatic number of some families of graphs , 2006, Discret. Math..

[15]  Brice Effantin,et al.  The b-chromatic number of some power graphs , 2003 .

[16]  Mekkia Kouider,et al.  Some bounds for the b-chromatic number of a grap , 2002, Discret. Math..

[17]  Tarek A. El-Ghazawi,et al.  A self-stabilizing distributed algorithm for spanning tree construction in wireless ad hoc networks , 2003, J. Parallel Distributed Comput..

[18]  Pradip K. Srimani,et al.  A self-stabilizing distributed algorithm for minimal spanning tree problem in a symmetric graph , 1998 .

[19]  David Manlove,et al.  The b-chromatic Number of a Graph , 1999, Discret. Appl. Math..

[20]  Brice Effantin.  The b-chromatic number of power graphs of complete caterpillars , 2005 .

[21]  Hamamache Kheddouci,et al.  A Distributed Algorithm for a b-Coloring of a Graph , 2006, ISPA.