Backbone Colorings for Networks

We study backbone colorings, a variation on classical vertex colorings: Given a graph G=(V,E) and a spanning subgraph H (the backbone) of G, a backbone coloring for G and H is a proper vertex coloring V →{ 1,2,... } in which the colors assigned to adjacent vertices in H differ by at least two. We concentrate on the cases where the backbone is either a spanning tree or a spanning path.

[1]  R. Möhring.  Algorithmic graph theory and perfect graphs , 1986 .

[2]  Jirí Fiala,et al.  Online and Offline Distance Constrained Labeling of Disk Graphs , 2001, ESA.

[3]  Jirí Fiala,et al.  Distance Constrained Labeling of Precolored Trees , 2001, ICTCS.

[4]  G. Wegner.  Graphs with given diameter and a coloring problem , 1977 .

[5]  Mohammad R. Salavatipour,et al.  A bound on the chromatic number of the square of a planar graph , 2005, J. Comb. Theory, Ser. B.

[6]  Russell Merris,et al.  Split graphs , 2003, Eur. J. Comb..

[7]  Paul G. Spirakis,et al.  Hardness Results and Efficient Appromixations for Frequency Assignment Problems and the Radio Coloring Problem , 2001, Bull. EATCS.

[8]  Magnús M. Halldórsson,et al.  Coloring powers of planar graphs , 2000, SODA '00.

[9]  W. K. Hale.  Frequency assignment: Theory and applications , 1980, Proceedings of the IEEE.

[10]  Jan van den Heuvel,et al.  Graph labeling and radio channel assignment , 1998, J. Graph Theory.

[11]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[12]  Jan van Leeuwen,et al.  lambda-Coloring of Graphs , 2000, STACS.

[13]  J. V. D. Heuvel,et al.  Graph labeling and radio channel assignment , 1998 .

[14]  Jerrold R. Griggs,et al.  Labelling Graphs with a Condition at Distance 2 , 1992, SIAM J. Discret. Math..

[15]  Hajo Broersma,et al.  Stars and bunches in planar graphs. Part II: General planar graphs and colourings , 2002 .

[16]  Hajo Broersma,et al.  Stars and bunches in planar graphs. Part I: Triangulations , 2002 .

[17]  Sophie Tison,et al.  Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science , 2000 .

[18]  Gerard J. Chang,et al.  The L(2, 1)-Labeling Problem on Graphs , 1996, SIAM J. Discret. Math..