ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2018-2019): c. 84%

Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 31(4) (2011) 675-686
DOI: 10.7151/dmgt.1572

Oriented colouring of some graph products

N.R. Aravind

The Institute of Mathematical Sciences
Taramani, Chennai, India

N. Narayanan

C R RAO Advanced Institute for Mathematics
Statistics and Computer Science
University of Hyderabad Campus, Hyderabad, India

C.R. Subramanian

The Institute of Mathematical Sciences
Taramani, Chennai, India


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

Keywords: oriented colouring

2010 Mathematics Subject Classification: 05C15, 05C20.


[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 E. 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 E. 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, E. 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 E. 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 E. 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 E. 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]E. 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]E. Sopena, Oriented graph coloring, Discrete Math. 229 (2001) 359--369, doi: 10.1016/S0012-365X(00)00216-8.

Received 5 March 2010
Revised 11 October 2010
Accepted 11 October 2010