ArticleOriginal scientific text

Title

Oriented colouring of some graph products

Authors 1, 2, 1

Affiliations

  1. The Institute of Mathematical Sciences, Taramani, Chennai, India
  2. C R RAO Advanced Institute for Mathematics, Statistics and Computer Science, University of Hyderabad Campus, Hyderabad, India

Abstract

We obtain some improved upper and lower bounds on the oriented chromatic number for different classes of products of graphs.

Keywords

oriented colouring

Bibliography

  1. N.R. Aravind and C.R. Subramanian, Forbidden subgraph colorings and the oriented chromatic number, in: 4th International Workshop on Combinatorial Algorithms 4393 (2009) 477-488.
  2. O.V. Borodin, A.V. Kostochka, J. Nesetril, A. Raspaud and É. Sopena, On the maximum average degree and the oriented chromatic number of a graph, Discrete Math. 206 (1999) 77-89, doi: 10.1016/S0012-365X(98)00393-8.
  3. O.V. Borodin, A.V. Kostochka, A. Raspaud and É. Sopena. Acyclic colouring of 1-planar graphs, Discrete Appl. Math. 114 (2001) 29-41, doi: 10.1016/S0166-218X(00)00359-0.
  4. B. Courcelle, The monadic second order logic of graphs. vi. on several representations of graphs by relational structures, Discrete Appl. Math. 54 (1994) 117-149, doi: 10.1016/0166-218X(94)90019-1.
  5. L. Esperet and P. Ochem, Oriented colorings of 2-outerplanar graphs, Information Processing Letters 101 (2007) 215-219, doi: 10.1016/j.ipl.2006.09.007.
  6. G. Fertin, A. Raspaud and A. Roychowdhury, On the oriented chromatic number of grids, Information Processing Letters 85 (2003) 261-266, doi: 10.1016/S0020-0190(02)00405-2.
  7. E. Fried, On homogeneous tournaments, Combinatorial Theory and its Applications 2 (1970) 467-476.
  8. P. Hell and J. Nesetril, Graphs and Homomorphisms, Oxford Lecture Series in Mathematics and its Applications (28), 2004.
  9. T. Herman, I. Pirwani and S. Pemmaraju, Oriented edge colorings and link scheduling in sensor networks, in: SENSORWARE 2006: 1st International Workshop on Software for Sensor Networks, 2006.
  10. W. Imrich and S. Klavžar, Product Graphs : Structure and Recognition (John Wiley & Sons, Inc., 2000).
  11. A.V. Kostochka, É. Sopena and X. Zhu, Acyclic and oriented chromatic numbers of graphs, J. Graph Theory 24 (1997) 331-340, doi: 10.1002/(SICI)1097-0118(199704)24:4<331::AID-JGT5>3.0.CO;2-P
  12. T.H. Marshall, Homomorphism bounds for oriented planar graphs, J. Graph Theory 55 (2007) 175-190, doi: 10.1002/jgt.20233.
  13. J. Nesetril, A. Raspaud and É. Sopena, Colorings and girth of oriented planar graphs, Discrete Math. 165-166 (1997) 519-530.
  14. P. Ochem, Oriented colorings of triangle-free planar graphs, Information Processing Letters 92 (2004) 71-76, doi: 10.1016/j.ipl.2004.06.012.
  15. A. Pinlou and É. Sopena, Oriented vertex and arc colorings of outerplanar graphs, Information Processing Letters 100 (2006) 97-104, doi: 10.1016/j.ipl.2006.06.012.
  16. A. Raspaud and É. Sopena, Good and semi-strong colorings of oriented planar graphs, Information Processing Letters 51 (1994) 171-174, doi: 10.1016/0020-0190(94)00088-3.
  17. É. Sopena, The chromatic number of oriented graphs, J. Graph Theory 25 (1997) 191-205, doi: 10.1002/(SICI)1097-0118(199707)25:3<191::AID-JGT3>3.0.CO;2-G
  18. É. Sopena, Oriented graph coloring, Discrete Math. 229 (2001) 359-369, doi: 10.1016/S0012-365X(00)00216-8.
Pages:
675-686
Main language of publication
English
Received
2010-03-05
Accepted
2010-10-11
Published
2011
Exact and natural sciences