Coloring the square of a planar graph

Journal of Graph Theory

Volumn 42, Issue 2, 2003, Pages 110-124

  Van den Heuvel, Jan ^a   McGuinness, Sean ^b  

^a LONDON SCHOOL OF ECONOMICS   (United Kingdom)

^b UMEÅ UNIVERSITY   (Sweden)

Author keywords

Chromatic number; Labeling of a graph; Planar graph

Indexed keywords

EID: 0037329128     PISSN: 03649024     EISSN: None     Source Type: Journal    
DOI: 10.1002/jgt.10077     Document Type: Article

References (17)

1. 1 G. Agnarsson and M. M. Halldórsson, Coloring Powers of planar graphs. Preprint ( 2000).
2. 2 K. Appel and W. Haken, Every planar map is four colourable. Part I: Discharging, Illinois J Math 21 ( 1977), 429–490.
3. 3 K. Appel, W. Haken, and J. Koch, Every planar map is four colourable. Part II: Reducibility, Illinois J Math 21 ( 1977), 491–567.
4. 4 O. V. Borodin, H. J. Broersma, A. Glebov, and J. van den Heuvel, Stars and bunches in planar graphs. Part I: Triangulations. CDAM Research Report Series 2002‐04 (2002). Original Russian version. In: Diskretn Anal Issled Oper Ser 1 8, no. 2 ( 2001), 15–39.
5. 5 O. V. Borodin, H. J. Broersma, A. Glebov, and J. van den Heuvel, Stars and bunches in planar graphs. Part II: General planar graphs and colourings. CDAM Research Report Series 2002‐05 (2002). Original Russian version. In: Diskretn Anal Issled Oper Ser 1 8, no. 4 ( 2001), 9–33.
6. 6 G. J. Chang, W.‐T. Ke, D. Kuo, D. D.‐F. Liu, and R. K. Yeh, On L (d,1)‐labellings of graphs. Discrete Mathematics, 220 ( 2000), 57–66.
7. 7 G. J. Chang and D. Kuo, The L(2,1)‐labelling problem on graphs, SIAM J Disc Math 9 ( 1996), 309–316.
8. 8 J. P. Georges and D. W. Mauro, Generalized vertex labellings with a condition at distance two, Congressus Numerantium 109 ( 1995), 141–159.
9. 9 J. P. Georges and D. W. Mauro, One the size of graphs labelled with a condition at distance two, J Graph Th 22 ( 1996), 47–57.
10. 10 J. R. Griggs and R. K. Yeh, Labelling graphs with a condition at distance 2, SIAM J Disc Math 5 ( 1992), 586–595.
11. 11 P. J. Heawood, Map colour theorem, Quart J Pure Appl MathS 24 ( 1890), 332–338.
12. 12 T. R. Jensen and B. Toft, Graph coloring problems, John‐Wiley & Sons, New York ( 1995).
13. 13 T. K. Jonas, Graph coloring analogues with a condition at distance two: L (2,1)‐labellings and list λ ‐labellings. Ph.D. Thesis, University of South Carolina ( 1993).
14. 14 M. Molloy and M. R. Salavatipour, A bound on the chromatic number of the square of a planar graph. Preprint, University of Toronto ( 2002).
15. 15 N. Robertson, D. Sanders, P. Seymour, and R. Thomas, The four‐colour theorem, J Comb Th 70 ( 1997), 2–44.
16. 16 D. Sakai, Labelling chordal graphs: Distance two condition, SIAM J Disc Math 7 ( 1994), 133–140.
17. 17 G. Wegner, Graphs with given diameter and a colouring problem. Preprint, University of Dortmund ( 1977).