Labelling planar graphs without 4-cycles with a condition on distance two

Discrete Applied Mathematics

Volumn 156, Issue 12, 2008, Pages 2241-2249

  Wang, Weifan ^a   Cai, Leizhen ^b  

^a ZHEJIANG NORMAL UNIVERSITY   (China)

^b CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Cycle; Distance; L (p, q) labelling; Planar graph

Indexed keywords

GRAPH THEORY;

CYCLE; DISTANCE; GRAPH G; L (P, Q)-LABELLING; MAXIMUM DEGREE; PLANAR GRAPH; PLANAR GRAPHS; POSITIVE INTEGERS;

CODES (SYMBOLS);

EID: 49149115109     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2007.05.061     Document Type: Article

References (26)

1. G. Agnarsson, M.M. Halldórsson, Coloring powers of planar graphs, in: Proceedings of the Eleventh Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2000), San Francisco 2000 pp. 654-671
2. Agnarsson G., and Halldórsson M.M. Coloring powers of planar graphs. SIAM J. Discrete Math. 16 (2003) 651-662
3. Appel K., and Haken W. Every planar graph is four colorable. Bull. Amer. Math. Soc. 82 (1976) 711-712
4. Bodlaender H.L., Kloks T., Tan R.B., and van Leeuwen J. Approximations for λ-coloring of graphs. In: Reichel H., and Tison S. (Eds). Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science. STACS 2000. Lecture Notes in Computer Science vol. 1770 (2000), Springer, Berlin 395-406
5. O.V. Borodin, H.J. Broersma, A. Glebov, J. van den Heuvel, Stars and bunches in planar graphs. Part II: General planar graphs and colourings, CDAM Research Report, London School of Economics, 2002, A translated and adapted version of a paper that appeared in Diskretn. Anal. Issled. Oper. Ser. 18 (2001) 9-33 (in Russian)
6. Calamoneri T., and Petreschi R. L (h, 1)-labelling subgraphs of planar graphs. J. Parallel Distrib. Comput. 64 3 (2004) 414-426
7. Chang G.J., and Guo D. The L (2, 1)-labeling problem on graphs. SIAM J. Discrete Math. 9 (1996) 309-316
8. Chang G.J., Ke W.-T., Kuo D., Liu D.D.-F., and Yeh R.K. On L (d, 1)-labeling of graphs. Discrete Math. 220 (2000) 57-66
9. Fritisch F., and Fritisch G. The Four-Color Theorem (1998), Springer, New York Inc.
10. Georges J.P., Mauro D.W., and Stein M.I. Labeling products of complete graphs with a condition at distance two. SIAM J. Discrete Math. 14 (2000) 28-35
11. Gonçalves D. On the L (p, 1)-labelling of graphs. Discrete Math. Theoret. Comput. Sci. AE (2005) 81-86
12. Griggs J.R., and Yeh R.K. Labelling graphs with a condition at distance 2. SIAM J. Discrete Math. 5 (1992) 586-595
13. Hale W.K. Frequency assignment: Theory and applications. Proc. IEEE 68 (1980) 1497-1514
14. He W., Hou X., Lih K., Shao J., Wang W., and Zhu X. Edge-partitions of planar graphs and their game coloring numbers. J. Graph Theory 41 (2002) 307-317
15. van den Heuvel J., and McGuinness S. Coloring the square of a planar graph. J. Graph Theory 42 (2003) 110-124
16. Král D., and Škrekovski R. A theorem about the channel assignment problem. SIAM J. Discrete Math. 16 (2003) 426-437
17. Lam P.B.C., Xu B., and Liu J. The 4-choosability of planar graphs without 4-cycles. J. Combin. Theory Ser. B 76 (1999) 117-126
18. Lih K., and Wang W. Coloring the square of an outerplanar graph. Taiwanese J. Math. 10 (2006) 1015-1023
19. 4-minor free planar graph. Discrete Math. 269 (2003) 303-309
20. Molloy M., and Salavatipour M.R. A bound on the chromatic number of the square of a planar graph. J. Combin. Theory Ser. B 94 (2005) 189-213
21. Sakai D. Labeling chordal graphs: Distance two condition. SIAM J. Discrete Math. 7 (1994) 133-140
22. Wang W. Edge-partitions of graphs of nonnegative characteristic and their game coloring numbers. Discrete Math. 306 (2006) 262-270
23. Wang W. The L (2, 1)-labelling of trees. Discrete Appl. Math. 154 (2006) 598-603
24. Wang W., and Lih K. Labeling planar graphs with conditions on girth and distance two. SIAM J. Discrete Math. 17 (2004) 264-275
25. G. Wegner, Graphs with given diameter and a coloring problem, Preprint, University of Dortmund, 1977
26. n and related graphs. SIAM J. Discrete Math. 8 (1995) 499-506