Distance constrained labelings of planar graphs with no short cycles

Discrete Applied Mathematics

Volumn 157, Issue 12, 2009, Pages 2634-2645

  Dvořák, Zdeněk ^a   Král', Daniel ^a   Nejedlý, Pavel ^a   Škrekovski, Riste ^b  

^a CHARLES UNIVERSITY   (Czech Republic)

^b UNIVERSITY OF LJUBLJANA   (Slovenia)

Author keywords

Distance constrained labeling; L (p, q) labeling; Planar graphs with no short cycles

Indexed keywords

DISTANCE CONSTRAINED LABELING; L (P, Q)-LABELING; LABELINGS; MAXIMUM DEGREE; PLANAR GRAPH; PLANAR GRAPHS WITH NO SHORT CYCLES; REGULAR TREE; SHORT CYCLE;

LABELING;

GRAPHIC METHODS; LABELING; MATHEMATICAL ANALYSIS; PROBLEM SOLVING;

EID: 66149180673     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2008.08.013     Document Type: Article

References (24)

1. G. Agnarsson, R. Greenlaw, M.M. Halldórsson, Powers of chordal graphs and their coloring, Congr. Numer. (in press)
2. Bella P., Král' D., Mohar B., and Quittnerová K. Labeling planar graphs with a condition at distance two. European J. Combin. 28 8 (2007) 2201-2239
3. Bodlaender H.L., Kloks T., Tan R.B., and van Leeuwen J. λ-coloring of graphs. In: Goos G., Hartmanis J., and van Leeuwen J. (Eds). Proc. STACS'00. LNCS vol. 1770 (2000), Springer 395-406
4. O. 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, 2002-05, 2002
5. Borodin O.V., Glebow A.N., Ivanova A.O., Neustroeva T.K., and Taskinov V.A. Dostatocnye uslovija 2-distancionnoj Δ + 1 raskrasivaetosti ploskich grafov. Sibirskie elektronnye matematiceskie izvestija 1 (2004) 129-141 (in Russian)
6. Chang G.J., Ke W.-T., Liu D.D.-F., and Yeh R.K. On L (d, 1)-labelings of graphs. Discrete Math. 3 1 (2000) 57-66
7. Chang G.J., and Kuo D. The L (2, 1)-labeling problem on graphs. SIAM J. Discrete Math. 9 2 (1996) 309-316
8. Dvořák Z., Král' D., Nejedlý P., and Škrekovski R. Coloring squares of planar graphs with girth six. European J. Combin. 29 4 (2008) 838-849
9. Fiala J., Kratochvíl J., and Kloks T. Fixed-parameter complexity of λ-labelings. Discrete Appl. Math. 113 1 (2001) 59-72
10. Fotakis D.A., Nikoletseas S.E., Papadopoulou V.G., and Spirakis P.G. NP-Completeness results and efficient approximations for radiocoloring in planar graphs. In: Rovan B. (Ed). Proc. MFCS'00. LNCS vol. 1893 (2000), Springer 363-372
11. Georges J.P., and Mauro D.W. Labeling trees with a condition at distance two. Discrete Math. 269 (2003) 127-148
12. Gonçalves D. On the L (p, 1)-labelling of graphs. Discrete Math. Theoret. Comput. Sci. AE (2005) 81-86
13. Griggs J.R., and Yeh R.K. Labeling graphs with a condition at distance 2. SIAM J. Discrete Math. 5 (1992) 586-595
14. van den Heuvel J., and McGuiness S. Colouring of the square of a planar graph. J. Graph Theory 42 (2003) 110-124
15. Hoffman A.J., and Singelton R.R. On Moore graphs of diameter two and three. IBM J. Res. Develop. 4 (1960) 497-504
16. J.-H. Kang, L (2, 1)-labeling of 3-regular Hamiltonian graphs (submitted for publication)
17. J.-H. Kang, L (2, 1)-labelling of 3-regular Hamiltonian graphs, Ph.D. Thesis, University of Illinois, Urbana-Champaign, IL, 2004
18. Král' D. An exact algorithm for channel assignment problem. Discrete Appl. Math. 145 2 (2004) 326-331
19. Král' D., and Škrekovski R. A theorem about the channel assignment problem. SIAM J. Discrete Math. 16 3 (2003) 426-437
20. Král' D. Coloring powers of chordal graphs. SIAM J. Discrete Math. 18 3 (2004) 451-461
21. McDiarmid C. On the span in channel assignment problems: Bounds, computing and counting. Discrete Math. 266 (2003) 387-397
22. 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
23. Sakai D. Labeling chordal graphs: Distance two condition. SIAM J. Discrete Math. 7 (1994) 133-140
24. Wang W.-F., and Lih K.-W. Labeling planar graphs with conditions on girth and distance two. SIAM J. Discrete Math. 17 2 (2003) 264-275